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

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

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

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

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

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

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

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

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

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

DOI： 10.1007/BF00939633

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

DOI： 10.1007/BF00940312

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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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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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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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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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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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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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：INST ENGINEERING TECHNOLOGY-IET  

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.

DOI： 10.1049/iet-cta.2015.0400

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

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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.

DOI： 10.1016/j.fss.2013.07.021

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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.

DOI： 10.1016/j.fss.2013.07.021

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

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.

DOI： 10.1080/02331934.2011.651471

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

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

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

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：HINDAWI PUBLISHING CORPORATION  

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.

DOI： 10.1155/2013/234681

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

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

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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.

DOI： 10.1016/j.fss.2011.09.010

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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.

DOI： 10.1016/j.fss.2011.09.010

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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

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

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

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

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

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

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

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

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

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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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

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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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：WORLD ACAD UNION-WORLD ACAD PRESS  

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

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

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

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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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

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

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

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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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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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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Total pages：viii, 433 p.   Language：English

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This paper contains a weak optimality notion for set optimization. We consider a new concept of approximate efficiency for set optimization in terms of conical intervals and conical distance by using Tanaka's approximate minimality for vector optimization. Also, we show in the last part minimal element theorems and a variational principle by using our optimality.

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This paper contains generalized alternative theorems via a set scalarization method based on set-relations. We introduce semidefinite system and its dual case as a supplementary result.

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DOI： 10.11511/jacc.57.0_1373

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This paper is concerned with positivity analysis for discrete-time descriptor systems with time delays. At first, an explicit solution of such systems is given by using z-transform and inverse z-transform. Then, a set of necessary and sufficient conditions for positivity of discrete-time descriptor systems with time delays is presented under some conditions. In addition, based on the obtained conditions for positivity, systems with strictly positive state variables are concerned. Necessary and sufficient conditions to check strict positivity of state variables are obtained. Finally, an example is given to illustrate the effectiveness of the obtained results.

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

本研究では制約集合が有界開凸集合の補集合とコンパクト凸集合の共通部分で表わされる2次計画問題に対し，KKT点列挙法を提案する．また，KKT点列挙法を用いた大域的最適化手法やその応用について説明する．

DOI： 10.11511/jacc.57.0_1373

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DOI： 10.1155/2013/895439

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DOI： 10.11509/sci.SCI10.0.293.0

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Language：Japanese   Publisher：The Institute of Systems, Control and Information Engineers  

In this study, we propose an inner approximation method for solving a DC programming problem with a reverse convex constraint defined by a bounded open convex set. It is shown that the algorithm has the global convergence by utilizing an approximation of the set by a sequence of polytopes from inside.

DOI： 10.11509/sci.SCI10.0.293.0

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In this study, we suggest four kinds of improvement indices based on careful study of the feasibility for inefficient DMUs to become an efficient unit in the CCR model with the minimal change of input and output values. Moreover, we propose an algorithm for calculating the proposed indices based on quadratic programming techniques. Furthermore, we propose four efficient measure models based on careful study of the feasibility.

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In this paper, we propose an inner approximation method for solving a Lipschitz optimization problem. In order to execute the algorithm, we transform a Lipschitz optimization problem into a problem constrained by a hemisphere. The algorithm utilizes an approximation of the hemisphere by a sequence of polytopes from inside. Moreover, in order to calculate vertices of polytopes effectively, the algorithm utilizes the adjacency relationships among vertices.

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DOI： 10.11509/sci.SCI09.0.165.0

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Other Link： http://hdl.handle.net/2433/140632

Publisher：The Institute of Systems, Control and Information Engineers  

本研究ではリプシッツ最適化問題の双対問題に対する外部近似法に基づく新たな逐次近似解法を提案する．本研究で提案するアルゴリズムはリプシッツ最適化問題を高次の球上での最適化問題に変換し，その双対問題の制約集合を凸多面体で外部近似することで大域的収束性が保証され，暫定解列の任意の集積点が対象問題の大域的最適解となることが示される．また，制約関数が凸関数で定義されている場合，暫定解の列を制約集合上に生成することができ，実行可能な近似解を求めることができる．

DOI： 10.11509/sci.SCI09.0.165.0

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

In this study, we propose an inner approximation method for solving a Lipschitz optimization problem. In order to execute the algorithm, we transform a Lipschitz optimization problem into a problem constrained by a hemisphere. The algorithm utilizes an approximation of the hemisphere by a sequence of polytopes from inside. Moreover, in order to calculate vertices of polytopes effectively, the algorithm utilizes the adjacency relationships among vertices.

DOI： 10.11511/jacc.52.0.138.0

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DOI： 10.11511/jacc.52.0.138.0

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Language：Japanese   Publisher：The Japan Joint Automatic Control Conference  

In this study, we suggest four kinds of improvement indices based on careful study of the feasibility for inefficient DMUs to become an efficient unit in the CCR model with the minimal change of input and output values.Moreover, we propose an algorithm for calculating the proposed indices based on quadratic programming techniques.Furthermore, we propose four efficient measure models based on careful study of the feasibility.

DOI： 10.11511/jacc.52.0.223.0

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DOI： 10.11511/jacc.52.0.223.0

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In this study, we propose computational method on several scalarizing functions for sets in a vector spaces. Classically, we use some types of scalarization methods for multiobjective programming problems. For two decades, some papers devoted in the fields of vector optimization and set-valued optimization were appeared with interesting results using nonlinear scalarizing functions with respect to some partial ordering introduced by a convex cone in a vector space. The aim of this paper is to introduce several useful scalarizing functions for sets and propose certain computational methods for them by global optimization technique.

DOI： 10.11511/jacc.52.0.137.0

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DOI： 10.11509/sci.SCI08.0.247.0

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Language：Japanese   Publisher：The Institute of Systems, Control and Information Engineers  

In this study, we propose an inner approximation method for solving a Lipschitz optimization problem. In order to execute the algorithm, we consider the projection of the feasible set on a ball. The algorithm utilizes an approximation of the ball by a sequence of polytopes from inside.

DOI： 10.11509/sci.SCI08.0.247.0

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DOI： 10.11509/sci.SCI07.0.209.0

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In this study, we propose an outer approximation method for a global optimization problem constrained by convex and concave functions. It is known that such a problem can be transformed into a d.c. programming problem. The proposed algorithm utilizes a sequence of convex polyhedral sets approximating the reverse convex set.

DOI： 10.11509/sci.SCI07.0.209.0

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DOI： 10.11509/sci.SCI06.0.77.0

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In this study, we propose a successive approximation method using quadratic functions approximating constraint functions for a d.c. programming problem. By analyzing the relation of eigen vectors of Hessian matrices of constraint functions, the direction searching a feasible solution of the problemis determined.

DOI： 10.11509/sci.SCI06.0.77.0

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DOI： 10.11509/sci.SCI05.0.28.0

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Publisher：The Institute of Systems, Control and Information Engineers  

本研究では D.C. 計画問題に対する逐次近似解法を提案します。従来、D.C. 計画問題に対し提案されている外部近似法に基づくアルゴリズムは有限回の反復で得られる近似解が実行可能領域に含まれるとはかぎりません。そこで、本研究では主問題に代わり逆凸制約を緩和した問題に対し、外部近似法に基づくアルゴリズムを適用することで実行可能領域に含まれる近似解を求める手法を提案します。また、その手法にペナルティ関数を導入し、より効率的に凸多面体実行可能領域を逐次近似するアルゴリズムを提案します。

DOI： 10.11509/sci.SCI05.0.28.0

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