Updated on 2024/05/19

写真a

 
TANAKA Tamaki
 
Organization
Academic Assembly Institute of Science and Technology Fundamental Sciences Professor
Graduate School of Science and Technology Fundamental Sciences Mathematical Science Professor
Faculty of Science Department of Science Professor
Title
Professor
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Degree

  • Doctor(Science) ( 1992.9   Niigata University )

  • Master of Science ( 1986.3   Niigata University )

Research Interests

  • Optimization theory

  • Operations Research

  • Set-valued Analysis

  • Set Optimization

  • Convex Analysis

  • Mathematical Programming

Research Areas

  • Informatics / Mathematical informatics  / Optimization Theory

  • Natural Science / Basic mathematics  / Mathematical Programming, Optimization Theory

  • Natural Science / Applied mathematics and statistics  / Mathematical Programming, Optimization Theory

  • Informatics / Computational science  / Mathematical Programming

Research History (researchmap)

  • Niigata University   Department of Science, Mathematics Program   Professor

    2017.4

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  • Niigata University   Graduate School of Science and Technology, Fundamental Sciences Mathematical Science   Professor

    2010.4

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  • Niigata University   Graduate School of Science and Technology Information Science and Engineering Mathematical Sciences   Professor

    2004.4 - 2010.3

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  • Niigata University   Faculty of Science Department of Mathematics   Professor

    2001.4 - 2017.3

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  • Niigata University   Graduate School of Science and Technology Information Science and Engineering   Professor

    2001.3 - 2004.3

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  • Hirosaki University, Faculty of Science and Technology   Professor

    1997.10 - 2001.2

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  • Hirosaki University, Faculty of Science   Associate Professor (as old post name)

    1995.10 - 1997.9

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  • Hirosaki University, Faculty of Science   Lecturer

    1993.4 - 1995.9

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  • Hirosaki University, Faculty of Science   Assistant

    1988.7 - 1993.3

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Research History

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences Mathematical Science   Professor

    2010.4

  • Niigata University   Faculty of Science Department of Mathematics   Professor

    2004.4

  • Niigata University   Academic Assembly Institute of Science and Technology Fundamental Sciences   Professor

    2004.4

  • Niigata University   Graduate School of Science and Technology Information Science and Engineering Mathematical Sciences   Professor

    2004.4 - 2010.3

  • Niigata University   Faculty of Science Department of Mathematics   Professor

    2001.4 - 2004.3

  • Niigata University   Graduate School of Science and Technology Information Science and Engineering   Professor

    2001.3 - 2004.3

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Professional Memberships

  • The International Society on Multiple Criteria Decision Making

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  • Pacific Optimization Research Activity Group

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  • The Mathematical Society of Japan

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  • The Operations Research Society of Japan

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  • Working Group on Generalized Convexity (WGGC)

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  • International Research Working Group in Nonlinear Analysis and Convex Analysis

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Qualification acquired

  • 高等学校教諭1級免許(数学)

  • 高等学校教諭2級免許(数学)

  • 中学校教諭1級免許(数学)

 

Papers

  • Semicontinuity of the composition of set-valued map and scalarization function for sets Invited Reviewed

    Koichiro Ike, Mengxue Liu, Yuto Ogata, Tamaki Tanaka

    Journal of Applied and Numerical Optimization   1 ( 3 )   267 - 276   2019.12

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    Authorship:Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Research Press  

    DOI: 10.23952/jano.1.2019.3.06

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  • Sublinear-like scalarization scheme for sets and its applications to set-valued inequalities Invited

    Ike, Koichiro, Ogata, Yuto, Tanaka, Tamaki, Yu, Hui

    Variational Analysis and Set Optimization: Developments and Applications in Decision Making   72 - 91   2019.7

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  • A Calculation Approach to Scalarization for Polyhedral Sets by Means of Set Relations Reviewed

    Hui Yu, Koichiro Ike, Yuto Ogata, Tamaki Tanaka

    TAIWANESE JOURNAL OF MATHEMATICS   23 ( 1 )   255 - 267   2019.2

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:MATHEMATICAL SOC REP CHINA  

    In this paper, we focus on certain functions as scalarization for six types of set relations and discuss calculation algorithms for them between polyhedral sets, while those between polytopes have been already investigated. A major difference between polyhedral sets and polytopes is in boundedness. Polyhedral sets are no longer necessarily bounded. Methods for calculating types (1), (2), (4), (6) are easily available by a similar way to existing ideas. However, those for types (3) and (5), which are actually the most famous and long-standing types, require some technical ways approaching to the value of them by using the fact that finitely generatedness and polyhedrality coincide and can be algorithmically switched in finite-dimensional spaces. As a result, we show all types are reduced to a finite number of linear programming problems. Also, we demonstrate our methods through an example and give detailed calculation process.

    DOI: 10.11650/tjm/180703

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  • An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets Reviewed

    Yuto Ogata, Tamaki Tanaka, Yutaka Saito, Gue Myung Lee, Jae Hyoung Lee

    OPTIMIZATION   67 ( 7 )   1067 - 1075   2018

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:TAYLOR & FRANCIS LTD  

    This paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions.

    DOI: 10.1080/02331934.2018.1426582

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  • Convex-cone-based comparisons of and difference evaluations for fuzzy sets Reviewed

    Koichiro Ike, Tamaki Tanaka

    OPTIMIZATION   67 ( 7 )   1051 - 1066   2018

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:TAYLOR & FRANCIS LTD  

    This paper focuses on how to compare two fuzzy sets and, from the viewpoint of set optimization, proposes eight types of fuzzy-set relations based on a convex cone as new comparison criteria of fuzzy sets. Then, difference evaluation functions for fuzzy sets are introduced. Under suitable assumptions of certain compactness and stability of fuzzy sets, we show that these functions correspond well to the fuzzy-set relations. In addition, through transforming these functions stepwise, we deal with numerical calculation methods of them in particular cases. Consequently, we can judge whether each fuzzy-set relation holds or not for given two fuzzy sets with the aid of computers.

    DOI: 10.1080/02331934.2018.1432608

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  • Computational methods for set-relation-based scalarizing functions Reviewed International coauthorship International journal

    Hui Yu, Koichiro Ike, Yuto Ogata, Yutaka Saito, Tamaki Tanaka

    Nihonkai Mathematical Journal   28 ( 2 )   139 - 149   2017.8

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    Authorship:Last author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Niigata University  

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  • Sublinear scalarization methods for sets with respect to set-relations Reviewed

    Yuto Ogata, Yutaka Saito, Tamaki Tanaka, Syuuji Yamada

    Linear and Nonlinear Analysis   3 ( 2 )   121 - 132   2017.3

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  • CONVEXITY FOR COMPOSITIONS OF SET-VALUED MAP AND MONOTONE SCALARIZING FUNCTION Reviewed

    Shogo Kobayashi, Yutaka Saito, Tamaki Tanaka

    PACIFIC JOURNAL OF OPTIMIZATION   12 ( 1 )   43 - 54   2016.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:YOKOHAMA PUBL  

    In this paper, we give some characterization on several types of cone-convexity and cone-concavity for compositions of a set-valued map and some kind of order-monotone scalarizing function for sets in a vector space.

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  • NONCONVEX SEPARATION FUNCTIONAL IN LINEAR SPACES WITH APPLICATIONS TO VECTOR EQUILIBRIA Reviewed

    Cesar Gutierrez, Vicente Novo, Juan Luis Rodenas-Pedregosa, Tamaki Tanaka

    SIAM JOURNAL ON OPTIMIZATION   26 ( 4 )   2677 - 2695   2016

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SIAM PUBLICATIONS  

    In this paper, the so-called nonconvex separation functional is studied in a real linear space not necessarily endowed with a topology. The essential properties of this functional, which are well known in the topological framework, are derived by using algebraic counterparts to the topological concepts of interior and closure. Finally, it is used to characterize, in the same algebraic setting and by scalarization, weak efficient solutions of vector equilibrium problems defined through algebraic solid ordering sets.

    DOI: 10.1137/16M1063575

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  • ON GENERALIZATION OF RICCERI'S THEOREM FOR FAN-TAKAHASHI MINIMAX INEQUALITY INTO SET-VALUED MAPS VIA SCALARIZATION Reviewed

    Yutaka Saito, Tamaki Tanaka, Syuuji Yamada

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   16 ( 1 )   9 - 19   2015

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:YOKOHAMA PUBL  

    In the paper, we propose Ricceri's theorem on Fan-Takahashi minimax inequality for set-valued maps by using the scalarization method proposed by Kuwano, Tanaka and Yamada, and we give a characterization of a certain set which plays an important role in Ricceri's theorem.

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  • Relationships between vector-valued cone-dc and locally cone-dc functions Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   398 ( 2 )   588 - 593   2013.2

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this paper, we propose an extension for vector-valued cone-convex functions. Moreover, by utilizing the proposed extension, we show that each vector-valued locally cone-dc function defined over a compact convex set is cone-dc. (C) 2012 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2012.09.002

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  • Continuity of cone-convex functions Reviewed

    Issei Kuwano, Tamaki Tanaka

    OPTIMIZATION LETTERS   6 ( 8 )   1847 - 1853   2012.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER HEIDELBERG  

    In the paper, we show continuity of cone-convex set-valued maps by using nonconvex scalarization methods for sets.

    DOI: 10.1007/s11590-011-0381-4

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  • OPTIMALITY CONDITION FOR VECTOR-VALUED DC PROGRAMMING PROBLEMS Reviewed

    Mayumi Hojo, Tamaki Tanaka, Syuuji Yamada

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   13 ( 1 )   57 - 64   2012

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    In this paper, we introduce a general concept of the difference of two cone convex functions (DC function) in a different way from what Blanquero and Carrizosa [1] did. Also we show a certain optimality condition for dc programming by using some properties of DC functions.

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  • Dual and bidual problems for a Lipschitz optimization problem based on quasi-conjugation Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   378 ( 1 )   198 - 212   2011.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    In this paper, we consider a Lipschitz optimization problem (LOP) constrained by linear functions in R(n). In general, since it is hard to solve (LOP) directly. (LOP) is transformed into a certain problem (MP) constrained by a ball in R(n+1). Despite there is no guarantee that the objective function of (MP) is quasi-convex, by using the idea of the quasi-conjugate function defined by Thach (1991) [1], we can construct its dual problem (DP) as a quasi-convex maximization problem. We show that the optimal value of (DP) coincides with the multiplication of the optimal value of (MP) by -1. and that each optimal solution of the primal and dual problems can be easily obtained by the other. Moreover, we formulate a bidual problem (BDP) for (MP) (that is, a dual problem for (DP)). We show that the objective function of (BDP) is a quasi-convex function majorized by the objective function of (MP) and that both optimal solution sets of (MP) and (BDP) coincide. Furthermore, we propose an outer approximation method for solving (DP). (C) 2010 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2010.12.046

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  • Unified scalarization for Sets and Set-Valued Ky Fan Minimax Inequalities Invited Reviewed

    Issei Kuwano, Tamaki Tanaka, Syuuji Yamada

    Journal of Nonlinear and Convex Analysis   11 ( 3 )   513 - 525   2010.12

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  • Inherited Properties of Nonlinear Scalarizing Functions for Set-Valued Maps Reviewed

    Issei Kuwano, Tamaki Tanaka, Syuuji Yamada

    Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis   161 - 177   2010.12

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  • Cone-Semicontinuity of Set-Valued Maps by Analogy with Real-Valued Semicontinuity Reviewed

    Yuuya Sonda, Issei Kuwano, Tamaki Tanaka

    Nihonkai Mathematical Journal   21 ( 2 )   91 - 103   2010.12

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  • UNIFIED SCALARIZATION FOR SETS AND SET-VALUED KY FAN MINIMAX INEQUALITY Reviewed

    Issei Kuwano, Tamaki Tanaka, Syuuji Yamada

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   11 ( 3 )   513 - 525   2010

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    In the paper, we investigate some properties of nonlinear scalarizing functions for sets introduced by Kuwano, Tanaka, Yamada (2009) and prove four kinds of set-valued Ky Fan minimax inequality.

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  • MINIMAL ELEMENT THEOREM WITH SET-RELATIONS Reviewed

    Akira Shimizu, Tamaki Tanaka

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   9 ( 2 )   249 - 253   2008

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:YOKOHAMA PUBL  

    Hamel and Lohne proved the existence results for minimal points of subsets of the product space X x 2(Y), where X and Y are a separated uniform space and a topological vector space, respectively. In this paper, we present a similar minimal element theorem with set-relations to those introduced in [3].

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  • Alternative Theorems for Set-Valued Maps based on a Nonlinear Scalarization Invited Reviewed

    S.Nishizawa, M.Onodsuka, T.Tanaka

    Pacific Journal of Optimization   1 ( 1 )   147 - 159   2005.1

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  • On minimax and maximin values in multicriteria games Reviewed

    M Higuchi, T Tanaka

    MULTI-OBJECTIVE PROGRAMMING AND GOAL PROGRAMMING   141 - 146   2003

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER-VERLAG BERLIN  

    The paper is concerned with a multicriteria game whose payoff takes its values in an ordered vector space. As compare with usual single-criterion games, useful results in such classical games do not always hold as to multicriteria games. For example, minimax and maximin values are coincident under certain conditions in usual single-criterion games, but their values are not always coincident under similar conditions in multicriteria games. Therefore, in this paper, we propose a certain coincidence condition on minimax and maximin values under suitable setting in multicriteria games.

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  • Classification of Matrices by means of Envelopes for Bicriteria Matrix Games Invited Reviewed

    M.Higuchi, T.Tanaka

    International Journal of Mathematics, Game Theory, and Algebra   12 ( 5 )   371 - 378   2002.12

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  • On Vector Equilibrium Problems: Remarks on a General Existence Theorem and Applications Reviewed

    E.M.Kalmoun, H.Riahi, T.Tanaka

    Nihonkai Mathematical Journal   12 ( 2 )   149 - 164   2001.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Niigata University  

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  • Fan's inequality for set-valued maps Reviewed

    PG Georgiev, T Tanaka

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   47 ( 1 )   607 - 618   2001.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:PERGAMON-ELSEVIER SCIENCE LTD  

    We consider four variants of Fan's type inequality for vector-valued multifunctions in topological vector spaces with respect to a cone preorder in the target space. In order to establish these results, firstly we prove a two-function result of Simons directly by the scalar Fan's inequality, after that, by its help we derive a new two-function result, which is the base of our proofs.

    DOI: 10.1016/S0362-546X(01)00205-X

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  • Vector-Valued Set-Valued Variants of Ky Fan's Inequality Reviewed

    P.G.Georgiev, T.Tanaka

    Journal of Nonlinear and Convex Analysis   1 ( 3 )   245 - 254   2000.12

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  • Fan's inequalities for vector-valued multifunctions Reviewed

    PG Georgiev, T Tanaka

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   76 ( 9 )   153 - 157   2000.11

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:JAPAN ACAD  

    We present four variants of Fan's type inequality for vector-valued multifunctions in topological vector spaces with respect to a cone preorder in the target space, when the functions and the cone possess various kinds of semicontinuity and convexity properties. Using the classical scaler Fan inequality, we prove directly a two-function result of Simons, which is used to establish our main tool for proving: the presented results.

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  • On cone convexity of set-valued maps Reviewed

    D Kuroiwa, T Tanaka, XDH Truong

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   30 ( 3 )   1487 - 1496   1997.12

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  • Generalized semicontinuity and existence theorems for cone saddle points Reviewed

    T Tanaka

    APPLIED MATHEMATICS AND OPTIMIZATION   36 ( 3 )   313 - 322   1997.11

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER VERLAG  

    This paper is concerned with existence theorems for generalized saddle points (cone saddle points) of vector-valued functions. A concept of lower semicontinuity for vector-valued functions is introduced and its properties are investigated. Previous results of the author are extended by using the lower semicontinuity.

    DOI: 10.1007/s002459900065

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  • Cone-Quasiconvexity of Vector-Valued Functions

    T.Tanaka

    弘前大学理科報告   42 ( 1 )   157 - 163   1995.8

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (bulletin of university, research institution)   Publisher:Hirosaki University, Faculty of Science  

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  • GENERALIZED QUASICONVEXITIES, CONE SADDLE-POINTS, AND MINIMAX THEOREM FOR VECTOR-VALUED FUNCTIONS Reviewed

    T TANAKA

    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   81 ( 2 )   355 - 377   1994.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:PLENUM PUBL CORP  

    We establish the following theorems: (i) an existence theorem for weak type generalized saddle points; (ii) an existence theorem for strong type generalized saddle points; (iii). a generalized minimax theorem for a vector-valued function. These theorems are generalizations and extensions of the author's recent results. For such extensions, we propose new concepts of convexity and continuity of vector-valued functions, which are weaker than ordinary ones. Some of the proofs are bawd on a few key observations and also on the Browder coincidence. theorem or the Tychonoff fixed-point theorem. Also, the minimax theorem follows from the existence theorem for weak type generalized saddle points. The main spaces with mathematical structures considered are real locally convex spaces and real ordered topological vector spaces.

    DOI: 10.1007/BF02191669

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  • THE CONVEXITY OF A-ASSURES AND B-ASSURES INTA+B = INT(A+B) Reviewed

    T TANAKA, D KUROIWA

    APPLIED MATHEMATICS LETTERS   6 ( 1 )   83 - 86   1993.1

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    The aim of this paper is to call attention to some elementary properties of convex sets for the core operator and the interior operator in a linear space and a linear topological space, respectively.

    DOI: 10.1016/0893-9659(93)90154-F

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  • A Characterization of Generalized Saddle Points for Vector-Valued Functions via Scalarization Reviewed International journal

    T.Tanaka

    Nihonkai Mathematical Journal   1 ( 2 )   209 - 227   1990.12

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Niigata University, Department of Mathematics  

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  • EXISTENCE THEOREMS FOR CONE SADDLE POINTS OF VECTOR-VALUED FUNCTIONS IN INFINITE-DIMENSIONAL SPACES Reviewed

    T TANAKA

    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   62 ( 1 )   127 - 138   1989.7

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    DOI: 10.1007/BF00939633

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  • SOME MINIMAX PROBLEMS OF VECTOR-VALUED FUNCTIONS Reviewed

    T TANAKA

    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   59 ( 3 )   505 - 524   1988.12

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    DOI: 10.1007/BF00940312

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  • Optimality and duality for complex multi-objective programming Invited Reviewed International coauthorship International journal

    Tone-Yau Huang, Tamaki Tanaka

    Numerical Algebra, Control & Optimization   12 ( 1 )   121 - 134   2022.3

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:American Institute of Mathematical Sciences (AIMS)  

    <p xml:lang="fr">&lt;p style='text-indent:20px;'&gt;We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.&lt;/p&gt;

    DOI: 10.3934/naco.2021055

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  • Triple-hierarchical problems with variational inequality Reviewed International coauthorship International journal

    Thanyarat JItpeera, Tamaki Tanaka, Poom Kumam

    Numerical Algebra, Control & Optimization   2022

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:American Institute of Mathematical Sciences (AIMS)  

    <p xml:lang="fr">&lt;p style='text-indent:20px;'&gt;In this paper, we suggest and analyze an iterative scheme for finding the triple-hierarchical problem in a real Hilbert space. We also consider the strong convergence for the proposed method under some assumptions. Our results extend ones of Ceng et. al (2011) [&lt;xref ref-type="bibr" rid="b2"&gt;2&lt;/xref&gt;], Yao et. al (2011) [&lt;xref ref-type="bibr" rid="b24"&gt;24&lt;/xref&gt;].&lt;/p&gt;

    DOI: 10.3934/naco.2021038

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  • Multi-objective Optimization Problems with SOS-convex Polynomials over an LMI Constraint Reviewed

    Liguo Jiao, Jae Hyoung Lee, Yuto Ogata, Tamaki Tanaka

    TAIWANESE JOURNAL OF MATHEMATICS   24 ( 4 )   1021 - 1043   2020.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:MATHEMATICAL SOC REP CHINA  

    In this paper, we aim to find efficient solutions of a multi-objective optimization problem over a linear matrix inequality (LMI in short), in which the objective functions are SOS-convex polynomials. We do this by using two scalarization approaches, that is, the 6-constraint method and the hybrid method. More precisely, we first transform the considered multi-objective optimization problem into their scalar forms by the 6-constraint method and the hybrid method, respectively. Then, strong duality results, between each formulated scalar problem and its associated semidefinite programming dual problem, are given, respectively. Moreover, for each proposed scalar problem, we show that its optimal solution can be found by solving an associated single semidefinite programming problem, under a suitable regularity condition. As a consequence, we prove that finding efficient solutions to the considered problem can be done by employing any of the two scalarization approaches. Besides, we illustrate our methods through some nontrivial numerical examples.

    DOI: 10.11650/tjm/191002

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  • Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps Reviewed

    Nithirat Sisarat, Rabian Wangkeeree, Tamaki Tanaka

    JOURNAL OF GLOBAL OPTIMIZATION   77 ( 2 )   273 - 287   2020.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    This paper deals with a convex vector optimization problem with set-valued maps. In the absence of constraint qualifications, it provides, by the scalarization theorem, sequential Lagrange multiplier conditions characterizing approximate weak Pareto optimal solutions for the problem in terms of the approximate subdifferentials of the marginal function associated with corresponding set-valued maps. The paper shows also that this result yields the approximate Lagrange multiplier condition for the problem under a new constraint qualification which is weaker than the Slater-type constraint qualification. Illustrative examples are also provided to discuss the significance of the sequential conditions.

    DOI: 10.1007/s10898-019-00864-0

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  • ON IMAGES OF LINE-SEGMENTS BY VECTORIAL MATRICES Reviewed

    Kenji Kimura, Tamaki Tanaka

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   19 ( 10 )   1685 - 1694   2018

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:YOKOHAMA PUBL  

    Images of straight lines characterize some property of vectorial payoff matrix of multicriteria matrix game. In the paper, we consider what condition guarantees a vectorial matrix transfers a straight line to a straight line again. We also consider, in general, what kind of shape the image of a straight line by a vectorial matrix is.

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  • ON SOME GENERALIZATIONS OF EKELAND'S VARIATIONAL PRINCIPLE AND FIXED POINT THEOREMS IN QUASI-PARTIAL METRIC SPACES Reviewed

    Chirasak Mongkolkeha, Tamaki Tanaka, Poom Kumam

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   18 ( 11 )   2083 - 2099   2017

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:YOKOHAMA PUBL  

    Recently, Karapinar et.al. [13] introduced the concept of quasi-partial metric space and proved some generalized fixed point theorems in the space. In this paper, we prove some generalized Ekeland's variational principle and fixed point theorems for a Kanan type mapping in a quasi-partial metric space. Moreover, we also give some examples for our results.

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  • H-infinity control via dynamic output feedback for positive systems with multiple delays Reviewed

    Qingling Zhang, Youmei Zhang, Baozhu Du, Tamaki Tanaka

    IET CONTROL THEORY AND APPLICATIONS   9 ( 17 )   2574 - 2580   2015.11

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    This study is concerned with H-infinity control problems for positive systems with time delays using dynamic output feedback. Novel bounded real lemma for continuous-time systems with time delays is first presented, which shows one of the remarkable properties of diagonal positive definite matrix solutions to linear matrix inequalities for positive systems. The proposed results reveal that H-infinity norms of positive systems with time delays in state and output equations are equivalent to that of the corresponding systems with zero delays. The positivity preserving H-infinity control problem by means of dynamic output feedback is also considered, and thus necessary and sufficient conditions in the forms of matrix equalities are established for the solvability of such problem. The desired controller gains can be obtained by means of cone complementarity linearisation techniques. A numerical example is finally given to illustrate the effectiveness of the obtained results.

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  • Bounded real lemmas for positive descriptor systems Reviewed

    Qingling Zhang, Youmei Zhang, Tamaki Tanaka, Xinggang Yan

    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS   352 ( 1 )   346 - 368   2015.1

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    A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs). In this paper, based on the positivity characterization, a novel bounded real lemma for continuous positive descriptor systems in terms of strict LMI is first established by the separating hyperplane theorem. The result developed here provides a necessary and sufficient condition for systems to possess H-infinity norm less than gamma and shows the existence of PDDM solution. Moreover, under certain condition, a simple model reduction method is introduced, which can preserve positivity, stability and H-infinity norm of the original systems. An advantage of such method is that systems' matrices of the reduced order systems do not involve solving of LIVIEs conditions. Then, the obtained results are extended to discrete case. Finally, a numerical example is given to illustrate the effectiveness of the obtained results. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

    DOI: 10.1016/j.jfranldin.2014.10.019

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  • Positivity of Continuous-Time Descriptor Systems With Time Delays Reviewed

    Youmei Zhang, Qingling Zhang, Tamaki Tanaka, Xing-Gang Yan

    IEEE TRANSACTIONS ON AUTOMATIC CONTROL   59 ( 11 )   3093 - 3097   2014.11

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    This technical note is concerned with positivity characteristic of continuous-time descriptor systems with time delays. First, a set of necessary and sufficient conditions is presented to check the property. Then, considering a descriptor time-delay system with two assumptions, a new time-delay system is established whose positivity is equivalent to that of the original system. Furthermore, a set of necessary and sufficient conditions is provided to check the positivity of the new system. Finally, a numerical example is given to illustrate the validity of the results obtained.

    DOI: 10.1109/TAC.2014.2321233

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  • Positivity of Continuous-Time Descriptor Systems With Time Delays Reviewed

    Youmei Zhang, Qingling Zhang, Tamaki Tanaka, Xing-Gang Yan

    IEEE TRANSACTIONS ON AUTOMATIC CONTROL   59 ( 11 )   3093 - 3097   2014.11

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    This technical note is concerned with positivity characteristic of continuous-time descriptor systems with time delays. First, a set of necessary and sufficient conditions is presented to check the property. Then, considering a descriptor time-delay system with two assumptions, a new time-delay system is established whose positivity is equivalent to that of the original system. Furthermore, a set of necessary and sufficient conditions is provided to check the positivity of the new system. Finally, a numerical example is given to illustrate the validity of the results obtained.

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  • On Lusin's theorem for non-additive measures that take values in an ordered topological vector space Reviewed

    Toshikazu Watanabe, Tamaki Tanaka

    FUZZY SETS AND SYSTEMS   244   41 - 50   2014.6

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    Lusin's theorem was established for real-valued monotone measures under an equivalent condition to Egoroff's theorem recently. In this paper, we show that the same result remains valid for non-additive measures that take values in an ordered topological vector space. We apply our result to several ordered topological vector spaces. (C) 2013 Elsevier B.V. All rights reserved.

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  • On Lusin's theorem for non-additive measures that take values in an ordered topological vector space Reviewed

    Toshikazu Watanabe, Tamaki Tanaka

    FUZZY SETS AND SYSTEMS   244   41 - 50   2014.6

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    Lusin's theorem was established for real-valued monotone measures under an equivalent condition to Egoroff's theorem recently. In this paper, we show that the same result remains valid for non-additive measures that take values in an ordered topological vector space. We apply our result to several ordered topological vector spaces. (C) 2013 Elsevier B.V. All rights reserved.

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  • Successive search methods for solving a canonical DC programming problem Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    OPTIMIZATION   63 ( 3 )   371 - 384   2014.3

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    In this article, we propose two successive search methods for solving a canonical DC programming problem constrained by the difference set between two compact convex sets in the case where the dimension number is greater than or equal to three. In order to find feasible solutions, the algorithms generate the directions based on a branch and bound procedure, successively. By exploring the provisional solutions throughout the intersection of the boundaries of two compact convex sets, both algorithms calculate an approximate solution.

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  • Admissibility for positive continuous-time descriptor systems Reviewed

    Youmei Zhang, Qingling Zhang, Tamaki Tanaka, Min Cai

    INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE   44 ( 11 )   2158 - 2165   2013.11

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    Positive descriptor systems are a new research branch in descriptor systems. This article is devoted to the study of the admissibility property for positive continuous-time descriptor systems. Based on Lyapunov inequality existed for stability of positive descriptor systems, we provide a necessary and sufficient condition to guarantee the admissibility via linear matrix inequalities (LMIs). Furthermore, a necessary and sufficient condition to guarantee the admissibility is established by means of generalised Lyapunov equation if c-monomial decomposition is applied to positive descriptor systems. Finally, examples are given to illustrate the validity of the results obtained.

    DOI: 10.1080/00207721.2012.685200

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  • Admissibility for positive continuous-time descriptor systems Reviewed

    Youmei Zhang, Qingling Zhang, Tamaki Tanaka, Min Cai

    INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE   44 ( 11 )   2158 - 2165   2013.11

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    Positive descriptor systems are a new research branch in descriptor systems. This article is devoted to the study of the admissibility property for positive continuous-time descriptor systems. Based on Lyapunov inequality existed for stability of positive descriptor systems, we provide a necessary and sufficient condition to guarantee the admissibility via linear matrix inequalities (LMIs). Furthermore, a necessary and sufficient condition to guarantee the admissibility is established by means of generalised Lyapunov equation if c-monomial decomposition is applied to positive descriptor systems. Finally, examples are given to illustrate the validity of the results obtained.

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  • Expansion of the cross-efficiency evaluation by using the equations forming the efficient frontier in DEA Reviewed

    S. Washio, S. Yamada, T. Tanaka, T. Tanino

    OPTIMIZATION METHODS & SOFTWARE   28 ( 4 )   889 - 899   2013.8

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    In this paper, we propose an algorithm to calculate cross-efficiency scores which used the equations forming the efficient frontier in data envelopment analysis (DEA). In many standard DEA models, each decision-making unit (DMU) is evaluated by using the advantageous weight for itself. Then, many DMUs are evaluated as efficient, and those efficient DMUs are not ranked by the models. The cross-efficiency evaluation is a method to rank DMUs by using the advantageous weights for all DMUs. Previously, the cross-efficiency scores based on different ideas are calculated by solving multiple linear or nonlinear programming problems. However, it is often hard to solve such a nonlinear programming problem. Therefore, by analysing the efficient frontier, we construct an algorithm to calculate alternative cross-efficiency scores.

    DOI: 10.1080/10556788.2012.750320

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  • Note on the Regularity of Nonadditive Measures Reviewed

    Toshikazu Watanabe, Syuji Yamada, Tamaki Tanaka

    JOURNAL OF APPLIED MATHEMATICS   2013   2013

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    We consider the regularity for nonadditive measures. We prove that the non-additive measures which satisfy Egoroff's theorem and have pseudometric generating property possess Radon property (strong regularity) on a complete or a locally compact, separable metric space.

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  • Internal Positivity Analysis for Continuous Descriptor Systems with Time Delays Reviewed

    Youmei Zhang, Qingling Zhang, Tamaki Tanaka

    2013 32ND CHINESE CONTROL CONFERENCE (CCC)   285 - 290   2013

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    This paper is devoted to the study of internal positivity property of continuous descriptor time-delay systems. A necessary and sufficient condition to check such property is presented. Furthermore, under certain assumptions, a necessary and sufficient condition is provided to guarantee internal positivity of the new system, whose such property is equivalent to that of the origin one. Finally, a numerical example is given to illustrate the effectiveness of the results obtained.

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  • H-infinity Control for Linear Positive Discrete-Time Systems Reviewed

    Youmei Zhang, Qingling Zhang, Tamaki Tanaka

    JOURNAL OF APPLIED MATHEMATICS   2013

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    This paper is concerned with H-infinity control for linear positive discrete-time systems. Positive systems are characterized by nonnegative restriction on systems' variables. This restriction results in some remarkable results which are available only for linear positive systems. One of them is the celebrated diagonal positive definite matrix solutions to some existed well-known results for linear systems without nonnegative restriction. We provide an alternative proof for criterion of H-infinity norm by using separating hyperplane theorem and Perron-Frobenius theorem for nonnegative matrices. We also consider H-infinity control problem for linear positive discrete-time systems via state feedback. Necessary and sufficient conditions for such problem are presented under controller gain with and without nonnegative restriction, and then the desired controller gains can be obtained from the feasible solutions.

    DOI: 10.1155/2013/576379

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  • On a sufficient condition of Lusin's theorem for non-additive measures that take values in an ordered topological vector space Reviewed

    Toshikazu Watanabe, Toshiharu Kawasaki, Tamaki Tanaka

    FUZZY SETS AND SYSTEMS   194   66 - 75   2012.5

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    Classical Lusin's theorem is extended for real-valued fuzzy measures under the weak null-additivity condition recently. In this paper, we show similar results for non-additive measures that take values in an ordered topological vector space. Firstly, we prove Lusin type theorem for weakly null-additive Borel measures that are continuous from above and possess an additional continuity property suggested by Sun in 1994. Secondly, we state another one for weakly null-additive fuzzy Borel measures. Our results are applicable to several ordered topological vector spaces. (C) 2011 Published by Elsevier B.V.

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  • On a sufficient condition of Lusin's theorem for non-additive measures that take values in an ordered topological vector space Reviewed

    Toshikazu Watanabe, Toshiharu Kawasaki, Tamaki Tanaka

    FUZZY SETS AND SYSTEMS   194   66 - 75   2012.5

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    Classical Lusin's theorem is extended for real-valued fuzzy measures under the weak null-additivity condition recently. In this paper, we show similar results for non-additive measures that take values in an ordered topological vector space. Firstly, we prove Lusin type theorem for weakly null-additive Borel measures that are continuous from above and possess an additional continuity property suggested by Sun in 1994. Secondly, we state another one for weakly null-additive fuzzy Borel measures. Our results are applicable to several ordered topological vector spaces. (C) 2011 Published by Elsevier B.V.

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  • Improvements by analyzing the efficient frontier in DEA Reviewed

    Satoshi Washio, Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    EUROPEAN JOURNAL OF OPERATIONAL RESEARCH   217 ( 1 )   173 - 184   2012.2

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    In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the CCR model with the minimal change of input and output values. Moreover, we propose an algorithm for calculating such improvements by applying quadratic programming techniques. Furthermore, since all equations constructing the efficient frontiers of the CCR and BCC models are necessary to execute the algorithm, we present a procedure for calculating them. (C) 2011 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.ejor.2011.09.002

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  • Improvements by analyzing the efficient frontier in DEA Reviewed

    Satoshi Washio, Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    EUROPEAN JOURNAL OF OPERATIONAL RESEARCH   217 ( 1 )   173 - 184   2012.2

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    In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the CCR model with the minimal change of input and output values. Moreover, we propose an algorithm for calculating such improvements by applying quadratic programming techniques. Furthermore, since all equations constructing the efficient frontiers of the CCR and BCC models are necessary to execute the algorithm, we present a procedure for calculating them. (C) 2011 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.ejor.2011.09.002

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  • On Regularity for Non-additive Measure Reviewed

    Toshikazu Watanabe, Tamaki Tanaka

    NONLINEAR MATHEMATICS FOR UNCERTAINTY AND ITS APPLICATIONS   100   69 - 75   2011

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    In this paper, we give a certain result on the regularity for nonadditive Borel measure under the conditions of weakly null additivity, a continuity from above, and a certain additional continuity.

    DOI: 10.1007/978-3-642-22833-9_8

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  • IMPROVEMENT INDICES KEEPING THE FEASIBILITY IN DATA ENVELOPMENT ANALYSIS Reviewed

    Satoshi Washio, Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   12 ( 1 )   29 - 48   2011

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    In this study, we propose a computational algorithm to determine the equations simultaneously, which define the efficient frontiers of the four types of DEA(Data Envelopment Analysis) models(the CRS, VRS, IRS and DRS models). By applying the algorithm, we calculate each efficiency score of all DMUs(Decision Making Units) and classify efficient DMUs into three types of RTS(Returns To Scale). Moreover, for each DMU which is not efficient in the CRS model, we present two kinds of improvements. One is for becoming an efficient unit in the CRS model. The other is for becoming an efficient unit in the CRS model over the PP(Production Possibility) set of the VRS model. For each type of improvements, we use an order matrix defined by the decision maker to calculate an improvement target contained in the PP sets of some models.

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  • On Lusin's Theorem for Non-additive Measure Reviewed

    Tamaki Tanaka, Toshikazu Watanabe

    NONLINEAR MATHEMATICS FOR UNCERTAINTY AND ITS APPLICATIONS   100   85 - 92   2011

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    In this paper, we prove Lusin's theorem remains valid for nonadditive Borel measure under the conditions of weakly null additivity, continuity from above and a certain additional continuity.

    DOI: 10.1007/978-3-642-22833-9_10

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  • On Lusin's Theorem for Non-additive Measure Reviewed

    Tamaki Tanaka, Toshikazu Watanabe

    NONLINEAR MATHEMATICS FOR UNCERTAINTY AND ITS APPLICATIONS   100   85 - 92   2011

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    In this paper, we prove Lusin's theorem remains valid for nonadditive Borel measure under the conditions of weakly null additivity, continuity from above and a certain additional continuity.

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  • OUTER APPROXIMATION METHOD INCORPORATING THE FERRARI'S METHOD FOR SOLVING A QUADRATIC DC PROGRAMMING PROBLEM Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   12 ( 1 )   17 - 27   2011

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    In this paper, we propose two kinds of successive approximation methods for solving a quadratic dc programming problem. One is the algorithm based on an outer approximation method. The algorithm calculates an approximate solution by constructing two cutting planes at each iteration. The second is the outer approximation algorithm incorporating the Ferrari's method. By utilizing the Ferrari's method, provisional solutions are updated effectively.

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  • IMPROVEMENT INDICES KEEPING THE FEASIBILITY IN DATA ENVELOPMENT ANALYSIS Reviewed

    Satoshi Washio, Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   12 ( 1 )   29 - 48   2011

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    In this study, we propose a computational algorithm to determine the equations simultaneously, which define the efficient frontiers of the four types of DEA(Data Envelopment Analysis) models(the CRS, VRS, IRS and DRS models). By applying the algorithm, we calculate each efficiency score of all DMUs(Decision Making Units) and classify efficient DMUs into three types of RTS(Returns To Scale). Moreover, for each DMU which is not efficient in the CRS model, we present two kinds of improvements. One is for becoming an efficient unit in the CRS model. The other is for becoming an efficient unit in the CRS model over the PP(Production Possibility) set of the VRS model. For each type of improvements, we use an order matrix defined by the decision maker to calculate an improvement target contained in the PP sets of some models.

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  • On Regularity for Non-additive Measure Reviewed

    Toshikazu Watanabe, Tamaki Tanaka

    NONLINEAR MATHEMATICS FOR UNCERTAINTY AND ITS APPLICATIONS   100   69 - 75   2011

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    In this paper, we give a certain result on the regularity for nonadditive Borel measure under the conditions of weakly null additivity, a continuity from above, and a certain additional continuity.

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  • Outer Approximation Methods Incorporating Lipschitz Optimization Techniques for Solving a DC Programming Problem Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis   417 - 432   2010.12

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  • On Generalizing Cammaroto-Chinni's Theorem Reviewed

    Yousuke Araya, Tamaki Tanaka

    Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis   29 - 35   2010.12

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  • On Saddle-Point Problems for Set-Valued Functions Reviewed

    Kenji Kimura, Tamaki Tanaka

    Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis   115 - 124   2010.12

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  • Outer Approximation Method Incorporating a Quadratic Approximation for a DC Programming Problem Reviewed

    S. Yamada, T. Tanaka, T. Tanino

    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   144 ( 1 )   156 - 183   2010.1

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    In this paper, we propose an outer approximation method using two quadratic functions approximating the constraint functions of a DC programming problem. By analyzing the relation among the eigenvectors of the Hessian matrices of the constraint functions, the search direction for a feasible solution of the problem is determined. Moreover, to avoid line searches along similar directions, we incorporate a penalty function method in the algorithm.

    DOI: 10.1007/s10957-009-9590-8

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  • A Dual Problem for a Lipschitz Optimization Problem Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    Proceedings of Asian Conference on Nonlinear Analysis and Optimization   2009.10

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  • Characterization of Nonlinear Scalarizing Functions for Set-Valued Maps Reviewed

    Issei Kuwano, Tamaki Tanaka, Syuuji Yamada

    Proceedings of Asian Conference on Nonlinear Analysis and Optimization   2009.10

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  • EXISTENCE OF VECTOR EQUILIBRIA VIA EKELAND'S VARIATIONAL PRINCIPLE Reviewed

    Yousuke Araya, Kenji Kimura, Tamaki Tanaka

    TAIWANESE JOURNAL OF MATHEMATICS   12 ( 8 )   1991 - 2000   2008.11

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    In this paper, we prove Ekeland's type of variational principle for a vector equilibrium problem, and present a Caristi-Kirk type fixed point theorem and an existence result for vector equilibrium solution.

    DOI: 10.11650/twjm/1500405131

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  • Outer Approximation Methods for Solving a Global Optimization Problem with Reverse Convex Constraints Reviewed

    Syuuji Yamada, Tamaki Tanaka, Tetsuzo Tanino

    Nonlinear Analysis and Convex Analysis   2008.11

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  • Iterative construction of fixed points of nonself-mappings in Banach spaces Reviewed

    Lu-Chuan Zeng, Tamaki Tanaka, Jen-Chih Yao

    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   206 ( 2 )   814 - 825   2007.9

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    The purpose of this paper is to study the iterative methods for constructing fixed points of nonself-mappings in Banach spaces. The concept of the class of asymptotically Q(G) -weakly contractive nonself-mappings is introduced and a new iterative algorithm for finding fixed points of this class of mappings is studied. Several strong convergence results on this algorithm are established under different conditions. (C) 2006 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.cam.2006.08.028

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  • On Generalizing Caristi's Fixed Point Theorem Reviewed

    Yousuke Araya, Tamaki Tanaka

    Proceedings of the Fourth International Conference on Nonlinear Analysis and Convex Analysis   41 - 46   2007.1

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  • Existence Results of Cone Saddle-Points for Vector-Valued Functions Reviewed

    K.Kimura, T.Tanaka

    Proceedings of the Fourth International Conference on Nonlinear Analysis and Convex Analysis   239 - 251   2007.1

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  • Optimality Conditions in Set-Valued Optimization using Nonlinear Scalarization Methods Reviewed

    A.Shimizu, S.Nishizawa, T.Tanaka

    Proceedings of the Fourth International Conference on Nonlinear Analysis and Convex Analysis   565 - 574   2007.1

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  • A characterization of efficient saddle point for set-valued maps Invited Reviewed

    Tamaki Tanaka, Syuuji Yamada

    Proceedings of the Second International Conference on Game Theory and Applications   183 - 185   2007

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    We introduce a certain mathematical methodology on the comparison between sets in an ordered vector space, and we consider its application to Multicriteria game theory. By using nonlinear scalarization methods for set-valued optimization problems, we obtain optimality conditions for efficient solutions of such Multicriteria optimization problems. As an application, we observe efficient-like concepts for saddle point of set-valued maps.

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  • Existence theorem of cone saddle-points applying a nonlinear scalarization Reviewed

    K Kimura, T Tanaka

    TAIWANESE JOURNAL OF MATHEMATICS   10 ( 2 )   563 - 571   2006.2

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    This paper is concerned with a nonlinear scalarization for vector-valued functions. We consider applying the scalarization to existence of cone saddle-points. Some properties of the scalarization about cone-continuity and cone-convexity are described and then as an application, an existence theorem for vector saddle-points is treated.

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  • Monotonically Upper Semicontinuity

    T.Suzuki, Y.Kimura, T.Tanaka

    Bulletin of the Kyusyu Institute of Techonology   52   29 - 34   2005.3

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  • Existence Result for Vector-Valued Saddle-Point Problem by Using Convex Envelope Reviewed

    K.Kimura, T.Tanaka

    Proceedings of the Third International Conference on Nonlinear Analysis and Convex Analysis   187 - 194   2004.12

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  • On Inherited Properties for Set-Valued Maps and Existence Theorems for Generalized Vector Equilibrium Problems Reviewed

    S.Nishizawa, T.Tanaka

    Journal of Nonlinear and Convex Analysis   5 ( 2 )   187 - 197   2004.8

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  • Existence Theorems of Saddle Points for Vector Valued Functions Reviewed

    K.Kimura, T.Tanaka

    Proceedings of the Second International Conference on Nonlinear Analysis and Convex Analysis   169 - 178   2003.2

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  • Multicriteria Two-Person Zero-Sum Matrix Games Reviewed

    M.Higuchi, T.Tanaka

    Proceedings of the Second International Conference on Nonlinear Analysis and Convex Analysis   97 - 105   2003.2

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  • On Inherited Properties of Set-Valued Maps Reviewed

    S.Nishizawa, T.Tanaka, P.G.Georgiev

    Proceedings of the Second International Conference on Nonlinear Analysis and Convex Analysis   341 - 350   2003.2

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  • On inherited properties for vector-valued multifunctions Reviewed

    S Nishizawa, T Tanaka, PG Georgiev

    MULTI-OBJECTIVE PROGRAMMING AND GOAL PROGRAMMING   215 - 220   2003

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER-VERLAG BERLIN  

    In this paper, we consider several kinds of convexity and semicontinuity of multifunctions with respect to ordering cones, and we investigate inherited properties of convexity and semicontinuity through scalarization of multifunctions. We introduce four kinds of scalarizing functions to characterize images of a multi-function by using Tchebyshev scalarization; these (real-valued) scalarizing functions have the same sorts of convexity and semicontinuity which correspond to those of parent multifunctions.

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  • On saddle points of multiobjective functions Reviewed

    K Kimura, EM Kalmoun, T Tanaka

    MULTI-OBJECTIVE PROGRAMMING AND GOAL PROGRAMMING   177 - 182   2003

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    This paper is concerned with existence theorems for cone-saddle points of vector-valued functions in finite dimensional Euclidean spaces. By means of vector variational-like inequalities, we first characterize a vector saddle point problem and obtain the existence result under some conditions on the subdifferentiable of the vector-valued function. The continuity and convexity assumptions on the objective function are then relaxed.

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  • Multipurpose decision-making in house plan by using AHP Reviewed

    BJ Zhang, H Liang, T Tanaka

    MULTI-OBJECTIVE PROGRAMMING AND GOAL PROGRAMMING   421 - 427   2003

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    In this paper, we suggest and analyze a new support system for easy decision-making on housing planing. Using this, users can analyze their preferences by themselves individually and can select optimal alternatives. The purpose of this paper is to propose a rational decision-making system in housing planing based on the AHP (Analytic Hierarchy Process). Then, we show how standard evaluation can be decided on the this system. In this paper, evaluation and election of the room arrangements is based on the information data came from users.

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  • The shapley value in totally convex multichoice games Reviewed

    DA Ayoshin, T Tanaka

    APPLIED MATHEMATICS LETTERS   13 ( 4 )   95 - 98   2000.5

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    In this paper, we introduce a class of totally convex multichoice cooperative games and prove that the Shapley value of such games is always in the core. (C) 2000 Elsevier Science Ltd. All rights reserved.

    DOI: 10.1016/S0893-9659(99)00216-5

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  • Classification of matrix types for multicriteria two-person zero-sum matrix games Reviewed

    T Tanaka, M Higuchi

    CONTROL APPLICATIONS OF OPTIMIZATION 2000, VOLS 1 AND 2   659 - 668   2000

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    The paper is concerned with multicriteria games, or games with a vector payoffs. The aim of this paper is to give structure information for the graph of a payoff function in two-person zero-sum matrix game with two 2 x 2 matrices by using computational program on computer. As a result, six different types of classification on matrices for such multicriteria matrix game is presented. Moreover, complete characterizations for such classification and some examples of illustrations for graphs of payoff functions are given. Copyright (C) 2000 IFAC.

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  • On Semicontinuity of Set-Valued Maps and Marginal Functions Reviewed

    Y.Kimura, K.Tanaka, T.Tanaka

    Nonlinear Anlysis and Convex Analysis - Proceedings of the International Conference   181 - 188   1999.10

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  • The Core and the Dominance Core in Multichoice Multistage Games with Coalitions in Matrix Form Reviewed

    D.A.Aechine, T.Tanaka

    Nonlinear Anlysis and Convex Analysis - Proceedings of the International Conference   110 - 117   1999.10

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  • An outer approximation algorithm guaranteeing feasibility of solutions and approximate accuracy of optimality Reviewed

    S Yamada, T Tanaka

    JOURNAL OF GLOBAL OPTIMIZATION   14 ( 3 )   267 - 281   1999.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:KLUWER ACADEMIC PUBL  

    We treat a concave programming problem with a compact convex feasible set. Assuming the differentiability of the convex functions which define the feasible set, we propose two solution methods. Those methods utilize the convexity of the feasible set and the property of the normal cone to the feasible set at each point over the boundary. Based on the proposed two methods, we propose a solution algorithm. This algorithm takes advantages over classical methods: (1) the obtained approximate solution is always feasible, (2) the error of such approximate value can be evaluated properly for the optimal value of such problem, (3) the algorithm does not have any redundant iterations.

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  • An outer approximation algorithm guaranteeing feasibility of solutions and approximate accuracy of optimality Reviewed

    S Yamada, T Tanaka

    JOURNAL OF GLOBAL OPTIMIZATION   14 ( 3 )   267 - 281   1999.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:KLUWER ACADEMIC PUBL  

    We treat a concave programming problem with a compact convex feasible set. Assuming the differentiability of the convex functions which define the feasible set, we propose two solution methods. Those methods utilize the convexity of the feasible set and the property of the normal cone to the feasible set at each point over the boundary. Based on the proposed two methods, we propose a solution algorithm. This algorithm takes advantages over classical methods: (1) the obtained approximate solution is always feasible, (2) the error of such approximate value can be evaluated properly for the optimal value of such problem, (3) the algorithm does not have any redundant iterations.

    DOI: 10.1023/A:1008343426871

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  • Existence Theorems for Cone Saddle Points and Vector-Valued Minimax Theorems Reviewed

    T.Tanaka

    Lecture Notes in Economics and Mathematical Systems (Advances in Multiple Objective and Goal Programming)   455   210 - 218   1997.12

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  • Multistage Games with Vector Payoffs Reviewed

    L.A.Petrosjan, T.Tanaka

    Nova Journal of Mathematics, Game Theory and Algebra   6 ( 1 )   97 - 102   1996.12

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  • On a Relationship between Ekeland's Algorithm and Infimal Convolutions

    T.Tanaka

    弘前大学理科報告   43 ( 2 )   223 - 230   1996.12

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  • Approximately efficient solutions in vector optimization Reviewed

    Tamaki Tanaka

    Journal of Multi-Criteria Decision Analysis   5 ( 4 )   271 - 278   1996

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    Language:English   Publishing type:Research paper (scientific journal)  

    An approach to approximating solutions in vector optimization is developed for vector optimization problems with arbitrary ordering cones. This paper presents a study of approximately efficient points of a given set with respect to a convex cone in an ordered Banach space. Existence results for such approximately efficient points are obtained. A domination property related to these existence results is observed and then it is proved that each element of a given set is approximated by the sum of a point in a convex cone inducing the ordering and a point in a finite set consisting of such approximately efficient points of the set. © 1996 John Wiley &amp
    Sons, Ltd.

    DOI: 10.1002/(SICI)1099-1360(199612)5:4<271::AID-MCDA114>3.0.CO;2-W

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  • A New Approach to Approximation of Solutions in Vector Optimization Problems Reviewed

    T.Tanaka

    Proceedings of the Third Conference of the Association of Asian-Pacific Operational Research Societies within IFORS   497 - 504   1995.2

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  • ANOTHER OBSERVATION ON CONDITIONS ASSURING INTA+B = INT(A+B) Reviewed

    T TANAKA, D KUROIWA

    APPLIED MATHEMATICS LETTERS   7 ( 1 )   19 - 22   1994.1

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    The aim of this paper is to give a new condition assuring corA + B = cor(A + B) and intA + B = int(A + B) in a linear space and a linear topological space, respectively. Moreover, this paper presents some observations on the previous results given by the authors.

    DOI: 10.1016/0893-9659(94)90046-9

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  • SOME GENERAL CONDITIONS ASSURING INTA + B = INT(A + B) Reviewed

    T TANAKA, D KUROIWA

    APPLIED MATHEMATICS LETTERS   6 ( 3 )   51 - 53   1993.5

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    The aim of this paper is to give a generalization of the authors' result, which showed that the convexity of sets A and B assures corA + B = cor(A + B) and intA + B = int(A + B) in a linear space and a linear topological space, respectively.

    DOI: 10.1016/0893-9659(93)90033-J

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  • 2-TYPES OF MINIMAX THEOREMS FOR VECTOR-VALUED FUNCTIONS Reviewed

    T TANAKA

    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS   68 ( 2 )   321 - 334   1991.2

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:PLENUM PUBL CORP  

    It seems that minimax theorems for vector-valued functions found in recent papers have something in common. Taking note of this, we improve several results in the author's recent works and state two types of minimax theorems for vector-valued functions. One theorem refers to functions with some special convexity properties; the other theorem refers to separated functions of the type f(x, y) = u(x) + v(y). The proofs are based on the existence of weak cone saddle points of f and on a condition about a pointed convex cone which induces a partial ordering in the image space of f. We need the condition (C/{0}) + cl C subset-of C, which implies the Sterna-Karwat condition for a convex cone C of a Hausdorff topological vector space.

    DOI: 10.1007/BF00941571

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  • Cone-Convexity of Vector-Valued Functions

    T.Tanaka

    弘前大学理科報告   37 ( 2 )   170 - 177   1990.12

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  • On Cone-Extreme Points in $R^{n}$

    T.Tanaka

    Science Reports of Niigata University, Series A (Mathematics)   23   13 - 24   1987.3

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (bulletin of university, research institution)   Publisher:Niigata University, Department of Mathematics  

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Books

  • 要点明解線形数学 三訂版

    田中, 環, 小島, 秀雄, 星, 明考, 折田, 龍馬, 印南, 信宏, 吉原, 久夫

    培風館  2022.4  ( ISBN:9784563012410

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    Total pages:x, 203p   Language:Japanese Book type:Textbook, survey, introduction

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  • 非線形解析学と凸解析学の研究 No.2114 : RIMS共同研究(公開型)

    田中 環( Role: Edit)

    京都大学数理解析研究所  2019.5 

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    Total pages:iv, 239p   Book type:Scholarly book

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  • 要点明解線形数学 改訂版

    印南, 信宏, 田中, 環, 小島, 秀雄, 星, 明考

    培風館  2016.2  ( ISBN:9784563012007

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    Total pages:viii, 178p   Language:Japanese Book type:Textbook, survey, introduction

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  • Nonlinear Analysis and Convex Analysis; RIMS Kôkyûroku, No.1923

    ( Role: Edit)

    2014.11 

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    Total pages:冊   Book type:Scholarly book

    CiNii Books

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  • Proceedings of the third Asian Conference on Nonlinear Analysis and Optimization

    Asian Conference on Nonlinear Analysis and Optimization, 明石, 重男, 高橋, 渉, 田中, 環

    Yokohama Publishers  2014  ( ISBN:9784946552496

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    Total pages:vi, 377 p.   Language:English

    CiNii Books

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  • Proceedings of the Sixth International Conference on Nonlinear Analysis and Convex Analysis

    高橋, 渉, 木村, 泰紀, 田中, 環, International Conference on Nonlinear Analysis and Convex Analysis( Role: Edit ,  1--432)

    Yokohama Publishers  2010  ( ISBN:9784946552410

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    Total pages:viii, 433 p.   Language:English

    CiNii Books

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  • Proceedings of the Fifth International Conference on Nonlinear Analysis and Convex Analysis

    Hsu, Sze-Bi, Lai, Hang-Chin, Lin, Lai-Jiu, 高橋, 渉, 田中, 環, International Conference on Nonlinear Analysis and Convex Analysis( Role: Edit ,  1--218)

    Yokohama Publishers  2009  ( ISBN:9784946552328

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    Total pages:iv, 218 p.   Language:English

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  • Proceedings of the Asian Conference on Nonlinear Analysis and Optimization, Matsue, Japan, 2008

    明石, 重男, 高橋, 渉, 田中, 環( Role: Edit ,  1--388)

    Yokohama Publishers  2009  ( ISBN:9784946552366

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    Total pages:vi, 387 p.   Language:English

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  • Proceedings of the Fourth International Conference on Nonlinear Analysis and Convex Analysis

    高橋, 渉, 田中, 環, International Conference on Nonlinear Analysis and Convex Analysis( Role: Edit ,  1--704)

    Yokohama Publishers  2007  ( ISBN:9784946552274

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    Total pages:viii, 702 p.   Language:English

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  • 非線形解析学と凸解析学の研究

    京都大学数理解析研究所, 田中, 環

    京都大学数理解析研究所  2004.4 

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    Total pages:3, 219p  

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  • Multi-objective programming and goal programming : theory and applications

    谷野, 哲三, 田中, 環, Masahiro Inuiguchi( Role: Edit ,  427)

    Springer-Verlag  2003  ( ISBN:3540006532

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    Total pages:xix, 427 p.   Language:English

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  • 非線形解析学と凸解析学の研究

    田中, 環, 高橋, 渉, 京都大学数理解析研究所( Role: Edit)

    京都大学数理解析研究所  2013.1 

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    Total pages:iv, 276p  

    CiNii Books

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  • 非線形解析学と凸解析学の研究

    京都大学数理解析研究所, 田中, 環

    京都大学数理解析研究所  2010.4 

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    Total pages:iii, 280p  

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  • 集合値写像の非線形スカラー化手法の研究と数理計画問題と統計科学への応用

    田中, 環

    [田中環]  2007.4 

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    Total pages:136p  

    CiNii Books

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  • 要点明解線形数学

    吉原, 久夫, 印南, 信宏, 田中, 環, 小島, 秀雄(数学)

    培風館  2006.3  ( ISBN:4563003611

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    Total pages:viii, 172p   Language:Japanese

    CiNii Books

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  • Proceedings of the Third International Conference on Nonlinear Analysis and Convex Analysis

    Wataru Takahashi, Tamaki Tanaka( Role: Edit ,  1--591)

    Yokohama Publishers  2004.12  ( ISBN:4946552154

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    Language:English

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  • ベクトル最適化の解析的研究と数理計画問題への応用

    田中, 環

    [田中環]  2004.3 

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    Total pages:120p  

    CiNii Books

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  • Proceedings of the third International Conference on Nonlinear Analysis and Convex Analysis

    高橋, 渉, 田中, 環

    Yokohama Publishers  2004  ( ISBN:4946552154

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    Total pages:vii, 591 p.   Language:English

    CiNii Books

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  • Proceedings of the Second International Conference on Nonlinear Analysis and Convex Analysis

    Wataru Takahashi, Tamaki Tanaka( Role: Edit ,  579)

    Yokohama Publishers  2003.2  ( ISBN:494655209X

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    Language:English

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  • Proceedings of the second International Conference on Nonlinear Analysis and Convex Analysis

    高橋, 渉, 田中, 環, International Conference on Nonlinear Analysis and Convex Analysis

    Yokohama Publishers  2003  ( ISBN:494655209X

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    Total pages:vii, 579 p.   Language:English

    CiNii Books

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  • Game Theory and Applications, Volume VIII

    L.A.Petrosjan, V.V.Mazalov( Role: Joint author ,  Classification of Matrices by means of Envelopes for Bicriteria Matrix Games, M.Higuchi and T.Tanaka, pp.43-52.)

    Nova Science Publishers  2002.12  ( ISBN:159033373X

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  • N.A.C.A.2001 : The second International conference on Nonlinear Analysis and Convex Analysis : Hirosaki University, Hirosaki, Japan. July 30-August 2, 2001. Conference Program

    International Conference on Nonlinear Analysis and Convex Analysis, 高橋, 渉, 田中, 環

    Hirosaki University  2001 

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    Total pages:8, 129 p.   Language:English

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  • New Frontiers of Decision Making for the Information Technology Era

    Yong Shi, Milan Zeleny( Role: Sole author ,  25)

    World Scientific Publishers  2000.5  ( ISBN:9810242999

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    Language:English

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  • Duality theory

    T.Tanaka( Role: Joint author)

    the Operations Research Society of Japan  2000.5  ( ISBN:4930793025

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    Language:Japanese Book type:Dictionary, encyclopedia

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  • Nonlinear Analysis and Convex Analysis --- Proceedings of the International Conference

    Wataru Takahashi, Tamaki Tanaka( Role: Edit ,  388)

    World Scientific Publishers  1999.10  ( ISBN:9810240740

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    Language:English

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  • 経営科学OR用語大事典(森村英典・刀根薫・伊理正夫 監訳)

    田中 環( Role: Joint author ,  (翻訳)項目「非線形計画法」(pp.485-495))

    朝倉書店  1999.1  ( ISBN:4254121318

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    Language:Japanese Book type:Dictionary, encyclopedia

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  • Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis : Niigata, Japan, 28-31 July, 1998

    International Conference on Nonlinear Analysis and Convex Analysis, 高橋, 渉, 田中, 環

    World Scientific  1999  ( ISBN:9810240740

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    Total pages:xi, 388 p.   Language:English

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  • Game Theory and Applications II

    L.A.Petrosjan, V.V.Mazalov( Role: Joint author ,  7)

    Nova Science Publishers  1996.12  ( ISBN:1560723904

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Awards

  • Fellow

    2021.4   The Operations Research Society of Japan  

    TANAKA Tamaki

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Research Projects

  • Set Optimization for sets with inferior-to-superior relationship and its applications to numerical analysis

    Grant number:21K03367

    2021.4 - 2025.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TANAKA Tamaki, YAMADA Syuuji, LIU Xuefeng

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    Authorship:Principal investigator 

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

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  • Effective procedures for speeding up global optimization algorithms for large-scale canonical dc quadratic programming problems

    Grant number:20K11688

    2020.4 - 2024.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    Syuuji Yamada, Tamaki Tanaka, Yutaka Saito

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    Authorship:Coinvestigator(s) 

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

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  • Study on Set-Valued Inequalities based on Set-Valued Analysis and Convex Analysis and its Applications to Optimization Problems

    Grant number:26400194

    2014.4 - 2017.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TANAKA Tamaki, TANINO Tetsuzo, MATSUSHITA Shinya, SUZUKI Satoshi, KIMURA Kenji, HIGUCHI Masakazu, KIMURA Yasunori, KUROIWA Daishi, YAMADA Syuuji

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    Authorship:Principal investigator 

    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

    In this study, we give several applications by using nonlinear scalarization methods for sets and proposed computational scheme for the scalarizing fucntions. This approach has been proposed in the previous study (research 21540121 supported by Grant-in-Aid for Scientific Research (C)). First, we clarified the inherited properties of the composite function of a monotonic scalarizing function and a sort of convex set-valued map systematically. As the results, we had several applications on certain generalization of Ricceri's nonlinear inequality to set-valued maps, alternative theorem for set-valued maps, and also we developed computational methods to evaluate the scalarizing functions and some construction of difference evaluation functions for fuzzy sets. Besides, we studied multicriteria two-persons zero-sum matrix games, algebraic properties of weak efficient solutions for sets, and hierarchical equilibrium problems including fixed-point problems.

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  • Research on unified criteria in set-valued programming and its application

    Grant number:25400205

    2013.4 - 2016.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    Kuroiwa Daishi, YAMAUCHI Takamitsu, MATSUSHITA Shin-ya, TANAKA Tamaki

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    Grant amount:\4940000 ( Direct Cost: \3800000 、 Indirect Cost:\1140000 )

    Set-valued optimization problems are represented by using set-valued functions as objective and constraint functions in order to express various ideas in the real world. The study of set-valued optimization problems is required in the sense of theory and applications. However there are mainly two types of criteria of the solutions of the problem, l and u-types criteria, and also there is another s-type criterion.
    In this study, we give a unified framework for such various criteria including l, u, and s-types ones, and we observed the existence of solutions of the problems, generalized notions of convexity for set-valued maps, applications for vector-optimization problems with uncertainty, and so on.

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  • 多目的配置問題の解析的研究と商品開発システムへの応用

    2010.4 - 2013.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    金 正道, 田中 環

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    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid)  Grant type:Competitive

    まず、ファジィ多目的配置問題の安定性を調べた。次に、メンバーシップ関数の集計関数に基づいた準凹性の一般化を提案し、その性質を調べた。次に、レベル集合を用いてファジィ集合列の極限およびファジィ集合値写像の極限と導写像を定義し、それら性質を調べた。これにより、解がファジィ集合として得られるファジィ数理計画問題のモデル構築や安定性や感度分析を考える場合に必要になるファジィ集合値解析の基礎理論が構築された。

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  • 集合値写像の非線形スカラー化手法の研究と数理計画への応用

    2009.4 - 2012.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    田中 環

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\3300000 ( Direct Cost: \2310000 、 Indirect Cost:\990000 )

    統一的非線形スカラー化関数の遺伝的性質を利用して,集合値写像に対するKy Fanのミニマックス不等式やEgoroffの定理とLusinの定理の一般化を行った。

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  • Computer-assisted proof for stationary solution existence of Navier-Stokes equation on 3D domain

    Grant number:18K03411

    2018.4 - 2021.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    LIU Xuefeng, TANAKA Tamaki

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    Authorship:Coinvestigator(s) 

    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

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  • A global optimization method for a reverse convex programming problem by listing FJ points

    Grant number:15K04994

    2015.4 - 2019.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    YAMADA SYUUJI, TANAKA Tamaki, TANINO tetsuzo

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    Authorship:Coinvestigator(s) 

    Grant amount:\4550000 ( Direct Cost: \3500000 、 Indirect Cost:\1050000 )

    In this study, we propose a global optimization method for a reverse convex quadratic programming problem (QRC) whose feasible set is expressed as the area excluded the interior of a convex set from another convex set. It is known that many global optimization problems can be transformed into such a problem. Iterative solution methods for solving (QRC) have been proposed by many researchers. In order to find an approximate solution of a globally optimal solution of (QRC), we introduce a procedure for listing KKT points of (QRC). By utilizing such a procedure, we can calculate all KKT points contained in the intersection of the boundaries of convex sets defining the feasible set. Further, we propose an algorithm for finding a globally optimal solution of (QRC) by incorporating such a procedure into a branch and bound procedure.

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  • Development of successive iteration methods utilizing partial separating hyperplanes for a global optimization problem with a reverse convex constraint

    Grant number:24540118

    2012.4 - 2015.3

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    YAMADA Syuuji, TANAKA Tamaki, TANINO Tetsuzo

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    Grant type:Competitive

    Grant amount:\3380000 ( Direct Cost: \2600000 、 Indirect Cost:\780000 )

    In this study, we consider a global optimization problem (GRC) with a reverse convex constraint. For (GRC), many approximation algorithms based on outer approximation methods and branch-and-bound procedures have been proposed. However, since the volume of data necessary for executing such algorithms increases in proportion to the number of iterations, such algorithms are not effective for large scale problems. Hence, to calculate an approximate solution of a large scale (GRC), we propose new iterative solution methods. To avoid the growth of data storage, the proposed methods find an approximate solution of (GRC) by rotating a partial separating hyperplane around a convex set defining the feasible set at each iteration. Moreover, in order to improve the computational efficiency of the proposed methods, we utilize the polar coordinate system. Moreover, we apply the proposed algorithms to optimize a linear function over a weakly efficient set of a multi-objective programming problem.

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  • 集合値計画法における制約想定と求解法の研究

    2010.4 - 2013.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    黒岩 大史, 田中 環

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    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid)  Grant type:Competitive

    集合値計画法における制約想定の研究を行い、集合値凸関数を用いた集合値計画問題に対する最弱の制約想定をはじめとして、いくつかの集合値計画問題に対する制約想定を導入した。また求解法に関して良設定の集合値計画問題の研究を行った。

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  • Analytic research of multicriteria location problems and applications to the system for developing new products

    Grant number:22510133

    2010 - 2012

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    KON Masamichi, TANAKA Tamaki, KUWANO Hiroaki

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    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

    First, we investigated the stability of the fuzzy multicriteria location problems. Next, we generalized the quasiconcavity of membership functions based on aggregation functions, and investigated the properties of the generalized quasiconcavity. Finally, we gave new definitions of the limit of sequences of fuzzy sets, the limit of fuzzy set-valued mappings, and the derivative of fuzzy set-valued mappings based on level sets of fuzzy sets. Then, we investigated their properties. The obtained results can be expected to be useful for analyzing the fuzzy mathematical models whose solutions are fuzzy sets.

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  • Research on constraint qualification and solution method for set optimization programming

    Grant number:22540133

    2010 - 2012

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    KUROIWA Daishi, TANAKA Tamaki, YAMAUCHI Takamitsu, MATSUSHITA Shin-ya

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    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

    We study constraint qualification for optimization problems whose objective maps are set-valued maps based on criteria called `set optimization.’ We propose certain constraint qualifications for set optimization problems including a set optimization problem whose objective and constraint functions are set -valued convex functions. Also we study solution methods for well-posed set optimization problems.

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  • Study on Nonlinear Scalarization Methods for Set-Valued Maps and its Applications into Mathematical Programming

    Grant number:21540121

    2009 - 2011

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TANAKA Tamaki, ISOGAI Eiichi, YAMADA Syuuji, TANINO Tetsuzo, KUROIWA Daishi

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    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

    In this study, we give theoretical analysis on nonlinear scalarization methods for sets, which has been introduced in the previous study(research 21540121 supported by Grant-in-Aid for Scientific Research(C)), and we research algorithm development for its numerical calculations and its applications. That is to say we derive several mathematical properties related to certain inequalities for set-valued maps by the help of classical theory through the use of the invariant property of some scalarization methods for set-relationship.

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  • 集合値計画法における微分概念の研究とその応用

    2007.4 - 2010.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    集合値最適化問題が表現でき、かつ集合値写像の微分概念が自然に定義できるように空間と位相を導入した。そして微分の計算や双対理論を構築するための新しい概念を定義し、解を求めるための方法をより明確にした。

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  • 集合値写像の非線形スカラー化手法の研究と数理計画への応用

    2007.4 - 2009.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    田中 環

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\3500000 ( Direct Cost: \2450000 、 Indirect Cost:\1050000 )

    本研究では, 集合値写像の非線形スカラー化手法の研究を行い, 新たに統一的非線形スカラー化手法を提案してその有効性を確認し, 数理計画問題への応用研究を行った。まず, 大域的最適化手法を応用して非線形スカラー化関数値の計算方法を提案し, 逐次数値計算によって近似するアルゴリズムを開発した。また, 統一的非線形スカラー化手法におけるスカラー化関数について単調性や凸性に関する遺伝性が成立していることを明らかにした。

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  • A notions of directional derivative for set-valued maps on set optimization programming and its applications

    Grant number:19540130

    2007 - 2009

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    KUROIWA Daishi, TANAKA Tamaki, YAMAUCHI Takamitsu, MATSUSHITA Shin-ya

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    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

    We study optimization problems whose objective maps are set-valued maps based on criteria called 'set optimization.' We introduce a quotient space of a family of sets with an equivalence relation, we show the set optimization problems are embedded in the space, and we consider methodology to find solutions.

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  • Study on Nonlinear Scalarization Methods for Set-Valued Maps and its Applications into Mathematical Programming

    Grant number:19540120

    2007 - 2008

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TANAKA Tamaki, ISOGAI Eiichi, YAMADA Syuuji, TANINO Tetsuzo

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    Grant amount:\4550000 ( Direct Cost: \3500000 、 Indirect Cost:\1050000 )

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  • 逐次解析手法による統計的逐次推定問題の研究

    2006.4 - 2008.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    磯貝 英一

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    Grant type:Competitive

    分担者を含めた研究代表者はこの研究課題において、いくつかの研究成果を得ることができた。代表者の得た主な研究成果は次のようなものである。

    1.指数分布における未知な位置母数と尺度母数の関数の逐次信頼区間問題を考えた。与えられた区間の幅と信頼係数をもつ信頼区間を最小の標本数で構成する場合、その最小標本数には未知な母数が含まれるため実際には利用できない。そこで、標本抽出を停止する停止規則を定義し、この停止規則を用いて得られた無作為標本に基づいて逐次推定量及び逐次信頼区間を構成した。このとき、区間の幅がゼロに近づくに従って逐次信頼区間の被覆確率が信頼係数に収束するという、漸近一致性を示すことができた。また、関数の具体例として位置母数と尺度母数との比を与え、逐次信頼区間の漸近一致性及び平均標本数の2次の漸近展開も求めた。この研究成果はFar East Journal of Theoretical Statistics, vol. 21, no. 2(2007)に掲載された。

    2.未知な平均

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  • 集合値写像の非線形スカラー化手法の研究と数理計画問題と統計科学への応用

    2005.4 - 2007.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    Grant amount:\3300000 ( Direct Cost: \3300000 )

    本研究では,ベクトル最適化の解析的研究を幅広く行い,集合値写像に対する非線形スカラー化関数の性質を解析し,数理計画問題やゲーム理論への応用研究と統計科学における多次元データへの応用研究を行った。

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  • Study on Nonlinear Scalarization Methods for Set-Valued Maps and its Applications into Mathematical Programming Problems and Statistical Science.

    Grant number:17540108

    2005 - 2006

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TANAKA Tamaki, ISOGAI Eiichi, YAMADA Syuuji, TANINO Tetsuzo

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    Grant amount:\3300000 ( Direct Cost: \3300000 )

    In this research, we have studied several kinds of themes on vector optimization and nonlinear scalarization methods for set-valued maps analytically and broadly, and then we have applied to multi-dimensional data in a statistical science.
    1.We presented six papers for fundamental researches on nonlinear scalarizing functions and its applied researches into game theory at the Fourth International Conferences on Nonlinear Analysis and Convex Analysis (NACA2005,Okinawa). The papers have been published in the (refereed) proceedings,2006. They are related to (i)Caristi's fixed point theorems for vector-valued functions, (ii)existence results of cone saddle-points for vector-valued functions by using the Fan-KKM lemma, (iii)optimality conditions for efficient solutions in set-valued vector optimization problems.
    2.As an application in mathematical programming, we researched outer approximation methods for global optimization problems with Associate Professor Yamada and Professor Tanino (Osaka University) jointly. Professor Tanino obtained chaos generator based on the affine scaling method for global optimization problems, and its paper was published.
    3.As an application into multi-dimensional data in a statistical science, Professor Isogai considered presumption problems of arbitrary and possibly non-smooth densities.
    4.In abroad, we presented our results in the 8-th International Symposium on Generalized Convexity/Monotonicity (Varese, Italy), the 3rd Sino-Japanese Optimization Meeting in the e-Business Era (SJOM 2005)(Singapore). We delivered invited talks at Chung Yuan Christian University, National Sun Yat-sen University, National Tsing-Hua University, Aletheia University, National Cheng Kung University, Changhua University of Education in Taiwan.
    5.In Japan, we presented our results in RIMS Symposium on Nonlinear Analysis and Convex Analysis (Kyoto University), the symposium on developments of mathematical decision and its application (Department of Economics at Nagasaki University), the symposium on decision to mathematical model and its application (Department of Science at Kochi University).

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  • 統計的遂次推定方式の有効性に関する研究

    2004.4 - 2006.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    Grant amount:\3500000 ( Direct Cost: \3500000 )

    研究代表者及び各分担者は直接的または間接的にこの研究課題に関する研究成果を得ることができた。代表者の得た主な研究成果は次のようなものである。

    1.指数分布の尺度母数のある関数について、最小リスク逐次点推定問題を考察した。損失関数として1標本当たりの費用が一定であるときの標本抽出費用と二乗誤差の和を考え、この平均損失であるリスクを最小にする標本数を使ってこの関数を推定することである。このとき、最小標本数には未知な尺度母数が含まれる。そこで、逐次推定方式を提案して、1標本当たりの費用が十分小さいときの平均標本数およびこの逐次推定方式によるリスクの2次の漸近展開を求めた。この研究成果はAustrian Journal of Statistics, Vol.33, No.3(2004)に掲載された。

    2.ともに未知な尺度母数をもつ二つの指数分布において、それら二つの尺度母数の関数を推定する問題を考察した。本論文では、与えられた区間幅と信頼係数をもつ信頼区間を最小の標本数で

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  • ベクトル最適化の解析的研究と数理計画問題への応用

    2001.4 - 2004.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    Grant amount:\3800000 ( Direct Cost: \3800000 )

    集合値写像の凸性と半連続性及びそれらの拡張概念に関して,非線形スカラー化関数の遺伝的性質を明らかにした。

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  • Analytical Study on Vector Optimization and its Applications into Mathematical Programming Problems

    Grant number:13640097

    2001 - 2003

    System name:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Research category:Grant-in-Aid for Scientific Research (C)

    Awarding organization:Japan Society for the Promotion of Science

    TANAKA Tamaki, KON Masamichi

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    Grant amount:\3800000 ( Direct Cost: \3800000 )

    In this research, we have studied several kinds of themes on vector optimization analytically and broadly and then we got some results on saddle point's existence, vector equilibrium problem, convexity and semicontinuity for set-valued maps under systematic research and investigation. Moreover, we have studied on efficient solutions of multicriteria location problems. The main results and presentations are as follows.
    1.We presented our results on characterization of efficient solutions and existence of cone saddle points at The Second and Third International Conferences on Nonlinear Analysis and Convex Analysis(NACA2001,NACA2003), held at Hirosaki University and Tokyo Institute of Technology, August 2001 and August 2003, respectively. We delivered invited talks on multicriteria minimax inequality which is fundamental for cone saddle point of vector-valued function at NACA2003 and Workshop on Nonlinear Analysis & Convex Analysis, November 2003. Moreover, we organized the Fifth International Conference on Multi-Objective Programming and Goal Programming : Theory & Applications(MOPGP'02) at Nara, June 2002, and we discussed several problems and topics in this meeting.
    2.We presented our results on several inherited properties of scalarizing functions from convexity and semicontinuity of set-valued maps at NACA2001, MOPGP'02, and NACA2003. These results were presented in RIMS Symposium on Nonlinear Analysis and Convex Analysis.
    3.We presented our results on multicriteria game at NACA2001,MOPGP'02, and NACA2003.
    4.We presented our results on multicriteria location problems at NACA2001 and NACA2003. These results were presented in RIMS Symposium on Nonlinear Analysis and Convex Analysis. We also presented them at the research group of "decision and OR" of the Operations Research Society of Japan, held at Fukui University of Technology.

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  • ベクトル最適化の解析的研究と多目的意思決定問題への応用

    1999.4 - 2001.3

    System name:科学研究費助成事業

    Research category:奨励研究(A)

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    Grant type:Competitive

    Grant amount:\1800000 ( Direct Cost: \1800000 )

    集合値写像の凸性と半連続性を利用して,変分不等式の一般化を得た。また,多目的行列ゲームの利得関数の形状分類を行い,その描画システムをUNIXとWindow上で構築しゲーム理論的解釈を与えた。

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  • ベクトル最適化の解析的研究と多目的意思決定問題への応用

    Grant number:11740053

    1999 - 2000

    System name:科学研究費助成事業 奨励研究(A)

    Research category:奨励研究(A)

    Awarding organization:日本学術振興会

    田中 環

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    Grant amount:\1800000 ( Direct Cost: \1800000 )

    本研究では,集合値写像の凸性と半連続性に関する性質を継続して解析すると同時に,この基礎研究をもとにして,集合値鞍点定理や集合値ミニマックス定理の研究とその多目的ゲーム理論への応用を試みた。得られた結果は以下の通りである。
    1.多目的ゲームの簡単な場合として,2目的2人零和行列ゲームの利得関数の像の形状の分類を数学的に正確に行った。これまでに未解決であった包絡線の形状をもつ場合の特徴付けを正確に行った。この結果については,ロシア・サンクトペテルブルグで開催された国際会議CAO2000において2000年7月に招待講演による発表を行い,その論文を投稿中である。発表では,UNIX上で開発したC言語プログラム資ノートパソコン上でも起動できるWindows用のVisual-Cプログラムに移植して行った。国内でも,2000年11月に京都大学数理解析研究所で発表を行った。
    2.ベクトル値関数の鞍点定理やミニマックス定理の体系的な結果をさらに洗練し,集合値鞍点定理や集合値ミニマックス定理の基礎となるKy Fanの不等式のベクトル値関数版と集合値関数版を得ることができた。この結果は,2000年7月にイタリアで開催された非線形解析学者国際連合会WCNA2000や2000年8月に京都大学数理解析研究所で発表を行った。
    3.上記の2で得られた結果の基礎理論の研究とアルゴリズムへの応用研究を行った。これらの結果は,2001年2月に京都大学で開催された数理解析研究所の共同研究集会で発表を行い,現在論文としてまとめている。

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  • ベクトル最適化問題の解析的研究とその応用

    1997.4 - 1999.3

    System name:科学研究費助成事業

    Research category:奨励研究(A)

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    Grant type:Competitive

    Grant amount:\2400000 ( Direct Cost: \2400000 )

    実数値関数の半連続性をベクトル値関数や集合値写像に拡張して,その解析的な性質を導き出した。同時に,多選択多段階ゲームや多目的ゲームへの応用を研究した。

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  • 非線形解析学と凸解析学に関する国際研究集会の企画準備

    1997.4 - 1998.3

    System name:科学研究費助成事業

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

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    Grant type:Competitive

    Grant amount:\3000000 ( Direct Cost: \3000000 )

    ・第1回企画会議を平成9年7月10日に新潟ワシントンホテルで開催した。主に新潟地区の研究協力者に本会議に参加してもらい、非線形解析学と凸解析学に関する国際研究集会の企画準備の内容の概要を理解していただいた。そして、本研究の年間計画を議論し立案した。具体的には、8月初旬に弘前で第1回研究協力者会議を開き、9月初旬に東京で第2回研究協力者会議を開くとともにRockafellar博士に来日してもらいサ-ベイを行ってもらい、年末か年始に新潟で第2回企画会議を行って、国際会議の運営委員会の発足を行うことなどが認められた。

    ・第1回研究協力者会議を平成9年8月1日及び2日に弘前大学で開催した。本研究の研究協力者として、寺澤達雄先生(新潟大学)、山崎稀嗣先生(島根大学)、稲田浩一先生(鹿児島大学)の3氏に本会議に参加してもらい、本研究集会の企画準備の内容を理解していただいた。そして、1998年国際会議の規模とテ-マ、各委員と役割分担、論文投稿方法および〆

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  • ベクトル最適化問題の解析的研究とその応用

    Grant number:09740129

    1997 - 1998

    System name:科学研究費助成事業 奨励研究(A)

    Research category:奨励研究(A)

    Awarding organization:日本学術振興会

    田中 環

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    Grant amount:\2400000 ( Direct Cost: \2400000 )

    本研究では、集合値写像の凸性と半連続性に関する性質を解析すると同時に、この基礎研究をもとにして、集合値鞍点定理や集合値ミニマックス定理の研究とその多規準ゲーム理論への応用を試みた。しかしながら、計算機による数値実験などは発表する結果までには至らなかった。主にまとめられた理論的な結果は以下の通りである。
    1. ベクトル値関数の鞍点定理やミニマックス定理の体系的な結果をさらに洗練し、2つの国際学会で発表した。その結果、この内の1つの国際学会(International Conference on Multiobjective Programmin gand Goal Programming)の組織委員に次年度から加わることになった。
    2. 集合値写像の半連続性に関する性質を実数値関数の上半連続性および下半連続性に対応する拡張の観点から解析し、実数値関数と集合値写像の合成関数に関する半連続性の連鎖性に関する結果を与えた。これは、国内で開催された国際研究集会で共同研究として発表した。論文は、その研究報告集に掲載される予定である。
    3. ロシアからの研究留学生との共同研究の下で、多段階決定ゲームや協力ゲームの基礎研究を行い、いくつかの新しい知見が得られ、国内の研究集会で発表すると同時に論文としてまとめた。論文は,現在投稿中である。これらの研究をもとに、多規準意思決定問題としてのベクトル最適化理論の多規準ゲーム理論への応用を研究中である。

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  • 非線形解析学と凸解析学に関する国際研究集会の企画準備

    Grant number:09894003

    1997

    System name:科学研究費助成事業 基盤研究(C)

    Research category:基盤研究(C)

    Awarding organization:日本学術振興会

    田中 環, 黒岩 大史, 田中 謙輔, 高橋 渉

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    Grant amount:\3000000 ( Direct Cost: \3000000 )

    ・第1回企画会議を平成9年7月10日に新潟ワシントンホテルで開催した。主に新潟地区の研究協力者に本会議に参加してもらい、非線形解析学と凸解析学に関する国際研究集会の企画準備の内容の概要を理解していただいた。そして、本研究の年間計画を議論し立案した。具体的には、8月初旬に弘前で第1回研究協力者会議を開き、9月初旬に東京で第2回研究協力者会議を開くとともにRockafellar博士に来日してもらいサーベイを行ってもらい、年末か年始に新潟で第2回企画会議を行って、国際会議の運営委員会の発足を行うことなどが認められた。
    ・第1回研究協力者会議を平成9年8月1日及び2日に弘前大学で開催した。本研究の研究協力者として、寺澤達雄先生(新潟大学)、山崎稀嗣先生(島根大学)、稲田浩一先生(鹿児島大学)の3氏に本会議に参加してもらい、本研究集会の企画準備の内容を理解していただいた。そして、1998年国際会議の規模とテーマ、各委員と役割分担、論文投稿方法および〆切日程、ホームページ、予算関連などが話し合われた。
    ・第2回研究協力者会議を平成9年9月5日に東京工業大学で開催した。本研究の研究協力者として、相川弘明先生(島根大学)、木内博文先生(東京工業大学)、横山一憲先生(新潟経営大学)の3氏と事務局となる大学院生らにも本会議に参加してもらい、本研究集会の企画準備の内容を理解していただいた。そして、会議案内の作成方法と配布先について検討がなされ、国際会議の運営委員会の発足やホームページの開設などについて話し合われた。同時に、Rockafellar氏による講演会も行われた。
    ・第2回企画会議を平成10年1月9日に新潟ワシントンホテルで開催した。そして、会議案内の作成、投稿状況、助成金への申請、外国人招待者旅費補助金、国際会議用ポスター、レクチャーノート作成、参加登録手続き、国際会議の運営委員会、ホームページの開設などについて報告・検討がなされた。

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  • ベクトル最適化問題の解析的研究とそのアルゴリズムの研究

    1996.4 - 1997.3

    System name:科学研究費助成事業

    Research category:奨励研究(A)

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    Grant type:Competitive

    Grant amount:\1100000 ( Direct Cost: \1100000 )

    ベクトル最適化問題の解析的基礎研究を行い,多規準ゲーム理論へ応用し,解の探索を行うアルゴリズムの研究を行った。

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  • ベクトル最適化問題の解析的研究とそのアルゴリズムの研究

    Grant number:08740129

    1996

    System name:科学研究費助成事業 奨励研究(A)

    Research category:奨励研究(A)

    Awarding organization:日本学術振興会

    田中 環

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    Grant amount:\1100000 ( Direct Cost: \1100000 )

    最適化理論全般に関連する凸解析及び錐解析に現れる解析的な性質を体系化するために、その最近の研究結果を論文の別刷りやコピーとして収集した。これらの資料をもとにして研究を行い、いくつかの新しい知見が得られ、大きく分けて以下の4つの結果が得られた。
    1.ベクトル値関数の拡張された半連続性の考察を経て、錐鞍点の存在性とベクトル値ミニマックス定理に関する解析的研究を行い、論文として発表することが出来た。これにより、ベクトル値関数に対するミニマックス定理の拡張が行え、順序錐に基づく順序空間での関数の半連続性を研究する契機ともなった。
    2.上記の1を基礎にして、ロシアの研究者と多目的繰り返しゲームに関する共同研究を行い、論文として発表することが出来た。
    3.上記の1と2に関する研究を一般の多目的ゲーム問題に応用するために、集合値写像の凸性や半連続性を考慮した集合値解析及び集合値最適化の研究を進めた結果、集合値写像の凸性に関する体系的な結果を得ることができ、論文として発表することが出来た。また、集合値写像の半連続性に関する新しい知見が得られ、実数値関数に関するmarginal関数の半連続性(sup型およびinf型写像に関する半連続性)の特徴付けを与えることができ、論文として発表することが出来た。
    4.ベクトル最適化問題のアルゴリズムの研究として、まず、Ekelandの定理に現れるアルゴリズムを明らかにし、その研究に基づいて一般のベクトル最適化問題のアルゴリズムを研究した。残念ながら理論的な解釈のみしか得られなかった。一方、有限次元問題については、多目的計画法に基づく計算機シミュレーションを郵便配達区画改善問題に適用し、独自の結果を得ることが出来た。

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  • ベクトル最適化問題の解析的研究と制御システムへの応用

    1995.4 - 1996.3

    System name:科学研究費助成事業

    Research category:奨励研究(A)

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    Grant type:Competitive

    Grant amount:\1200000 ( Direct Cost: \1200000 )

    最適化理論全般に関連する凸解析及び錐解析に現れる解析的な性質を体系化するために、その最近の研究結果を論文の別刷りやコピ-として収集した。これらの資料をもとにして研究を行い、いくつかの新しい知見が得られ、大きく分けて以下の3つの結果が得られた。

    1.ε-劣微分解析を取り入れたベクトル最適化問題の考察を経て、ベクトル最適化問題の近似解の解析的研究を行い、論文として発表することが出来た。これは、ベクトル最適化問題の近似解の解析的研究に関するユニ-クな取り組みであり、近似的有効解の存在性やその特徴付けが理論的に与えられた。

    2.ベクトル値関数に関する性質を凸性・準凸性及び半連続性についていろいろなクラス分けとそれらの間の関係についてさらに解析し、新しい錐鞍点の存在定理を証明した。また、昨年10月に来日したロシアの研究者との意見交換により、これらの結果を応用した共同研究を実現し、その研究を論文としてまとめた。この

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  • ベクトル最適化問題の解析的研究と制御システムへの応用

    Grant number:07740136

    1995

    System name:科学研究費助成事業 奨励研究(A)

    Research category:奨励研究(A)

    Awarding organization:日本学術振興会

    田中 環

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    Grant amount:\1200000 ( Direct Cost: \1200000 )

    最適化理論全般に関連する凸解析及び錐解析に現れる解析的な性質を体系化するために、その最近の研究結果を論文の別刷りやコピーとして収集した。これらの資料をもとにして研究を行い、いくつかの新しい知見が得られ、大きく分けて以下の3つの結果が得られた。
    1.ε-劣微分解析を取り入れたベクトル最適化問題の考察を経て、ベクトル最適化問題の近似解の解析的研究を行い、論文として発表することが出来た。これは、ベクトル最適化問題の近似解の解析的研究に関するユニークな取り組みであり、近似的有効解の存在性やその特徴付けが理論的に与えられた。
    2.ベクトル値関数に関する性質を凸性・準凸性及び半連続性についていろいろなクラス分けとそれらの間の関係についてさらに解析し、新しい錐鞍点の存在定理を証明した。また、昨年10月に来日したロシアの研究者との意見交換により、これらの結果を応用した共同研究を実現し、その研究を論文としてまとめた。この論文は、平成8年度の国際会議で発表する予定である。
    3.上の2に関する研究を微分ゲームや制御問題に応用するためには、集合値写像の凸性や半連続性を考慮した集合値解析及び集合値最適化を研究しなければならないことが明らかになった。これに従い、集合値写像の半連続性の非整合性を指摘し、その改良した概念とそれらの関係を明らかにした。これについては、京都大学数理解析研究所講究録に発表した。
    今後、集合値写像の凸性の理論的な調査研究をし、その結果に基づいて集合値解析及び集合値最適化の研究を行う予定である。

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  • ベクトル最適化問題の解析的研究とゲ-ム理論的応用

    1994.4 - 1995.3

    System name:科学研究費助成事業

    Research category:奨励研究(A)

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    Grant type:Competitive

    Grant amount:\1200000 ( Direct Cost: \1200000 )

    最適化理論全般に関連する凸解析及び錐解析に現れる解析的な性質を体系化するために、その最近の研究結果を論文の別刷りやコピ-として収集した。これらの資料をもとにして研究を行った結果、大きく分けて2つの新しい知見が得られた。

    一つは、ε-劣微分解析を取り入れたベクトル最適化問題の考察を行い、ベクトル最適化問題の近似解の解析的研究への応用を行ったことである。これは、ベクトル最適化問題の近似解の解析的研究に関するユニ-クな取り組みであり、近似的有効解の存在性やその特徴付けが理論的に与えられた。また、これまでに知られている近似解に比べて病的な例を除去した近似解の概念を提唱し、その有効性を検証した。

    もう一つは、ベクトル値関数に関する性質を凸性・準凸性及び半連続性についていろいろなクラス分けとそれらの間の関係について詳細に調べ、これを基に新しいタイプのベクトル値ミニマックス定理を証明した。これは、ベクトル最適

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  • ベクトル最適化問題の解析的研究とゲーム理論的応用

    Grant number:06740139

    1994

    System name:科学研究費助成事業 奨励研究(A)

    Research category:奨励研究(A)

    Awarding organization:日本学術振興会

    田中 環

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    Grant amount:\1200000 ( Direct Cost: \1200000 )

    最適化理論全般に関連する凸解析及び錐解析に現れる解析的な性質を体系化するために、その最近の研究結果を論文の別刷りやコピーとして収集した。これらの資料をもとにして研究を行った結果、大きく分けて2つの新しい知見が得られた。
    一つは、ε-劣微分解析を取り入れたベクトル最適化問題の考察を行い、ベクトル最適化問題の近似解の解析的研究への応用を行ったことである。これは、ベクトル最適化問題の近似解の解析的研究に関するユニークな取り組みであり、近似的有効解の存在性やその特徴付けが理論的に与えられた。また、これまでに知られている近似解に比べて病的な例を除去した近似解の概念を提唱し、その有効性を検証した。
    もう一つは、ベクトル値関数に関する性質を凸性・準凸性及び半連続性についていろいろなクラス分けとそれらの間の関係について詳細に調べ、これを基に新しいタイプのベクトル値ミニマックス定理を証明した。これは、ベクトル最適化のゲーム理論的応用と考えられ、これまでの著者のベクトル値ミニマックス定理が整理された。
    今回のこの後者の研究に対して、ロシアから招待講演の依頼があり、平成6年9月にオレホボ・ズエボ(Orekhovo-Zuevo)で開催された「不確実性の下での多基準問題について第3回国際研究集会」に組織委員として出席し、ベクトル値ミニマックス定理について45分の全体講演を行ってきた。
    ロシアでは、最適制御の立場から微分ゲームのベクトル版に関する研究が盛んであり、私のベクトル値ミニマックス定理は多くの注目を浴びた。しかも、この訪問を契機に自分のこれまでの研究の応用を微分ゲームに見いだすことが出来たのは、たいへん大きな収穫である。今後は、ロシアの研究者との共同研究などを通じて、ベクトルミニマックス理論を大きく発展させたいと願っている。

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  • ベクトル値ミニマックス理論の基礎的研究と多目的ゲームや多目的最適化問題への応用

    Grant number:02740095

    1990

    System name:科学研究費助成事業 奨励研究(A)

    Research category:奨励研究(A)

    Awarding organization:日本学術振興会

    田中 環

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    Grant amount:\700000 ( Direct Cost: \700000 )

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Teaching Experience (researchmap)

  • Introduction to Set and Topology A

    2020.10

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  • Introduction to Set and Topology B

    2020.10

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  • Study Skills for Science

    2019.4
    -
    2019.9

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  • Fundamentals of Mathematics B1

    2018.10

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  • Fundamentals of Mathematics B2

    2018.10

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  • Convex Analysis A

    2017.10

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  • Convex Analysis B

    2017.10

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  • Optimization Mathematics B

    2017.4

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  • Optimization Mathematics A

    2017.4

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  • Specialist Active Learnig (Mathematics)

    2017.4
    -
    2018.9

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  • Study Skills for Science

    2017.4
    -
    2017.9

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  • Primary Seminar VII

    2016.4
    -
    2017.9

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  • Primary Seminar VI

    2015.4
    -
    2015.9

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  • Spring Seminar in Taiwan I

    2014.10

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  • Spring Seminar in Taiwan II

    2014.10

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  • Theory II of Information processing systems

    2014.4
    -
    2016.9

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  • Mathmatical programming and LP

    2013.10
    -
    2017.3

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  • Information Technology and Society

    2012.4

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  • Advanced Mathematical Programming

    2007.10

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  • Fundamentals of Mathematics B

    2006.10
    -
    2013.3

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  • Introduction to Mathematical Programming

    2005.10

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  • Practice on Computer Network

    2004.10
    -
    2019.9

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  • Graph and Network Theory

    2004.10
    -
    2012.3

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  • Digital Presentation Methods

    2003.4
    -
    2014.9

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  • Digital Presentation Theory

    2003.4
    -
    2013.9

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  • Seminar in Mathematics

    2002.4

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  • 数理科学セミナーⅡ(数学)

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  • 数理科学セミナーⅡ(情報)

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  • 数理物質科学特定研究Ⅲ(数理科学)

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  • 数理科学博士セミナーⅢ

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  • リサーチキャンプ

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  • 数理科学文献詳読Ⅱ(情報)

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  • 数理科学セミナーⅠ(数学)

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  • 数理システム特論

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  • 凸解析学と最適化理論

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  • くらしと数理

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  • 基礎ゼミIII

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  • スタディ・スキルズ(数学学習法)

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  • OR基礎

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  • 自然科学総論Ⅰ

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  • スタディ・スキルズ(数学・情報学習法)

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  • 数理科学博士セミナーⅡ

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  • 数理科学研究発表〔外部発表〕(数学)

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  • 研究発表演習・発表

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  • 中間発表

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  • 数理科学研究発表演習〔外部発表〕(数学)

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  • 数理物質科学特定研究Ⅱ(数理科学)

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  • 数理科学コース演習

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  • 数理科学博士セミナーⅠ

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  • 数理科学研究発表演習〔中間発表〕(数学)

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  • 数理物質科学特定研究Ⅰ(数理科学)

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  • 数学の世界

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  • 数理物質科学特定研究Ⅱ(数学)

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  • 数理物質科学特定研究Ⅰ(数学)

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  • 数理科学文献詳読Ⅰ(数学)

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  • 数理科学文献詳読Ⅱ(数学)

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Teaching Experience

  • 応用数理特別講義

    2022
    Institution name:新潟大学

  • 台湾スプリングセミナー I

    2021
    Institution name:新潟大学

  • 台湾スプリングセミナー II

    2021
    Institution name:新潟大学

  • ネットワーク実習

    2021
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2021
    Institution name:新潟大学

  • 集合と位相入門B

    2020
    Institution name:新潟大学

  • 集合と位相入門A

    2020
    Institution name:新潟大学

  • 先端科学技術総論

    2020
    Institution name:新潟大学

  • 日本事情自然系A

    2019
    -
    2022
    Institution name:新潟大学

  • 数学基礎B2

    2018
    Institution name:新潟大学

  • 数学基礎B1

    2018
    Institution name:新潟大学

  • 最適化数学B

    2017
    Institution name:新潟大学

  • 凸解析学A

    2017
    Institution name:新潟大学

  • 最適化数学A

    2017
    Institution name:新潟大学

  • 凸解析学B

    2017
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2017
    -
    2021
    Institution name:新潟大学

  • 専門力アクティブ・ラーニング

    2017
    -
    2018
    Institution name:新潟大学

  • 基礎ゼミIII

    2017
    Institution name:新潟大学

  • 基礎ゼミVII

    2016
    Institution name:新潟大学

  • スタディ・スキルズ(数学・情報学習法)

    2015
    -
    2016
    Institution name:新潟大学

  • 数理科学研究発表〔外部発表〕(数学)

    2015
    Institution name:新潟大学

  • 自然科学総論Ⅰ

    2015
    Institution name:新潟大学

  • 基礎ゼミVI

    2015
    Institution name:新潟大学

  • 数理科学博士セミナーⅡ

    2015
    Institution name:新潟大学

  • 情報計画システムII

    2014
    -
    2016
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅱ(数理科学)

    2014
    Institution name:新潟大学

  • 研究発表演習・発表

    2014
    Institution name:新潟大学

  • 中間発表

    2014
    Institution name:新潟大学

  • 数理科学研究発表演習〔外部発表〕(数学)

    2014
    Institution name:新潟大学

  • 情報社会論

    2013
    Institution name:新潟大学

  • 台湾スプリングセミナー I

    2013
    -
    2018
    Institution name:新潟大学

  • 台湾スプリングセミナー II

    2013
    -
    2018
    Institution name:新潟大学

  • 情報計画システムI

    2013
    -
    2016
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅱ(数学)

    2013
    -
    2015
    Institution name:新潟大学

  • 数理科学コース演習

    2013
    -
    2015
    Institution name:新潟大学

  • 数理科学セミナーⅡ(数学)

    2013
    -
    2015
    Institution name:新潟大学

  • 数理科学博士セミナーⅠ

    2013
    -
    2015
    Institution name:新潟大学

  • 数理科学文献詳読Ⅱ(数学)

    2013
    -
    2015
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅰ(数理科学)

    2013
    -
    2015
    Institution name:新潟大学

  • 数理科学セミナーⅠ(数学)

    2013
    -
    2014
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅰ(数学)

    2013
    -
    2014
    Institution name:新潟大学

  • 数理科学文献詳読Ⅰ(数学)

    2013
    -
    2014
    Institution name:新潟大学

  • 数理科学研究発表演習〔中間発表〕(数学)

    2013
    -
    2014
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅲ(数理科学)

    2012
    -
    2015
    Institution name:新潟大学

  • リサーチキャンプ

    2012
    Institution name:新潟大学

  • 数理科学セミナーⅡ(情報)

    2012
    Institution name:新潟大学

  • 数学の世界

    2012
    Institution name:新潟大学

  • 数理科学博士セミナーⅢ

    2012
    Institution name:新潟大学

  • 数理科学文献詳読Ⅱ(情報)

    2012
    Institution name:新潟大学

  • 数理システム特論

    2011
    -
    2012
    Institution name:新潟大学

  • 凸解析学と最適化理論

    2009
    Institution name:新潟大学

  • くらしと数理

    2008
    -
    2009
    Institution name:新潟大学

  • 数学講究

    2007
    Institution name:新潟大学

  • 数理計画特論

    2007
    Institution name:新潟大学

  • 数理計画概論

    2007
    Institution name:新潟大学

  • ネットワーク実習

    2007
    -
    2018
    Institution name:新潟大学

  • スタディ・スキルズ(数学学習法)

    2007
    -
    2014
    Institution name:新潟大学

  • デジタル表現実習

    2007
    -
    2014
    Institution name:新潟大学

  • デジタル表現論

    2007
    -
    2013
    Institution name:新潟大学

  • 数学基礎B

    2007
    -
    2012
    Institution name:新潟大学

  • グラフとネットワーク理論

    2007
    -
    2011
    Institution name:新潟大学

  • OR基礎

    2007
    Institution name:新潟大学

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