Search Results 1-20 of 22

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  • Duality Theorems for Convex and Quasiconvex Set Functions

    Suzuki Satoshi , Kuroiwa Daishi

    … In mathematical programming, duality theorems play a central role. … Especially, in convex and quasiconvex programming, Lagrange duality and surrogate duality have been studied extensively. … A typical example of mathematical programming is a minimization problem of a real-valued function on a vector space. … However, duality theorems and its constraint qualifications for mathematical programming with set functions have not been studied yet. …

    SN Operations Research Forum (1), 2020-02-21

    IR 

  • Optimality Conditions and Constraint Qualifications for Quasiconvex Programming

    Suzuki Satoshi

    … In mathematical programming, various kinds of optimality conditions have been introduced. … Recently, by using Greenberg–Pierskalla subdifferential and Martínez-Legaz subdifferential, necessary and sufficient optimality conditions for quasiconvex programming have been introduced. … On the other hand, constraint qualifications are essential elements for duality theory in mathematical programming. …

    Journal of Optimization Theory and Applications 183(3), 963-976, 2019-12

    IR 

  • 準凸計画問題に対する劣微分を用いた最適性条件 (非線形解析学と凸解析学の研究)  [in Japanese]

    鈴木 聡 , 黒岩 大史

    … 特に近年筆者等によって示された, essentially quasiconvex programmingに対する最適性の必要十分条件, 一般の準凸計画問題に対する最適性の必要十分条件, 逆準凸制約を持つ準凸計画問題に対する最適性の必要条件について述べる. …

    数理解析研究所講究録 (2112), 154-159, 2019-04

    IR 

  • Characterizations of the solution set for non-essentially quasiconvex programming

    Suzuki Satoshi , Kuroiwa Daishi

    … Characterizations of the solution set in terms of subdifferentials play an important role in research of mathematical programming. … Recently, characterizations of the solution set for essentially quasiconvex programming in terms of Greenberg–Pierskalla subdifferential are studied by the authors. … Unfortunately, there are some examples such that these characterizations do not hold for non-essentially quasiconvex programming. …

    Optimization letters 11(8), 1699-1712, 2017-12

    IR 

  • Duality Theorems for Separable Convex Programming without Qualifications

    Suzuki Satoshi , Kuroiwa Daishi

    … In the research of mathematical programming, duality theorems are essential and important elements. … Recently, Lagrange duality theorems for separable convex programming have been studied. … Tseng proves that there is no duality gap in Lagrange duality for separable convex programming without any qualifications. … Jeyakumar and Li prove that Lagrange multiplier always exists without any qualifications for separable sublinear programming. …

    Journal of optimization theory and applications 172(2), 669-683, 2017-02

    IR 

  • Characterizations of the solution set for quasiconvex programming in terms of Greenberg-Pierskalla subdifferential

    Suzuki Satoshi , Kuroiwa Daishi

    … In convex programming, characterizations of the solution set in terms of the subdifferential have been investigated by Mangasarian. … In quasiconvex programming, how-ever, characterizations of the solution set by any solution point and an invariance property of Greenberg-Pierskalla subdifferential, which is one of the well known subdifferential for quasiconvex functions, have not been studied yet as far as we know. …

    Journal of Global Optimization 62(3), 431-441, 2015-07

    IR 

  • Surrogate duality for robust optimization

    Suzuki Satoshi , Kuroiwa Daishi , Lee Gue Myung

    … We prove surrogate duality theorems for robust quasiconvex optimization problems and surrogate min-max duality theorems for robust convex opti-mization problems. …

    European Journal of Operational Research 231(2), 257-262, 2013-12-01

    IR 

  • Some constraint qualifications for quasiconvex vector-valued systems

    Suzuki Satoshi , Kuroiwa Daishi

    … In this paper, we consider minimization problems with a quasiconvex vector-valued inequality constraint. … We propose two constraint quali12;cations, the closed cone constraint quali12;cation for vector-valued quasiconvex programming (the VQ-CCCQ) and the basic constraint quali12;cation for vector-valued quasicon-vex programming (the VQ-BCQ). …

    Journal of Global Optimization 55(3), 539-548, 2013-03

    IR 

  • Necessary and sufficient conditions for some constraint qualifications in quasiconvex programming

    Suzki Satoshi , Kuroiwa Daishi

    … In this paper, we investigate relations between constraint qualifications in quasiconvex programming. …

    Nonlinear Analysis : Theory, Methods & Applications 75(5), 2851-2858, 2012-03

    IR 

  • QUASICONVEX DUALITY THEOREMS WITH QUASICONJUGATES AND GENERATOR

    Suzuki Satoshi

    … This paper is based on the author's thesis, \On duality theorems for quasiconvex programming. … In this paper, we investigate duality theorems for quasiconvex programming as generalizations of results in convex programming, and consists of three topics. … The third is about constraint qualications for Lagrange-type duality theorem in quasiconvex programming. …

    Memoirs of the Faculty of Science and Engineering Shimane University. Ser. B, Mathematical Science -(45), 1-39, 2012-03

    IR 

  • Necessary and Sufficient Constraint Qualification for Surrogate Duality

    Suzuki Satoshi , Kuroiwa Daishi

    … In mathematical programming, constraint qualifications are essential elements for duality theory. …

    Journal of Optimization Theory and Applications 152(2), 366-377, 2012-02

    IR 

  • Subdifferential calculus for a quasiconvex function with generator

    Suzuki Satoshi , Kuroiwa Daishi

    … Recently, we discussed optimality conditions for quasiconvex programming by introducing 'Q-subdifferential', which is a notion of differential of quasiconvex functions. …

    Journal of Mathematical Analysis and Applications 384(2), 677-682, 2011-12-15

    IR 

  • Sandwich theorem for quasiconvex functions and its applications

    Suzuki Satoshi , Kurosiwa Daishi

    … In convex programming, sandwich theorem is very important because it is equivalent to Fenchel duality theorem. … In this paper, we investigate a sandwich theorem for quasiconvex functions. … Also, we consider some applications for quasiconvex programming. …

    Journal of Mathematical Analysis and Applications 379(2), 649-655, 2011-07-15

    IR 

  • On Set Containment Characterization and Constraint Qualification for Quasiconvex Programming

    Suzuki Satoshi , Kuroiwa Daishi

    Dual characterizations of the containment of a convex set with qua-siconvex inequality constraints are investigated. A new Lagrange-type duality and a new closed cone constraint qualification are desc …

    Journal of Optimization Theory and Applications 149(3), 554-563, 2011-06

    IR 

  • Optimality conditions and the basic constraint qualification for quasiconvex programming

    Suzuki Satoshi , Kuroiwa Daishi

    … In this paper, we consider optimality conditions and a constraint qualification for quasiconvex programming. … To the purpose, we introduce a generator and a new subdifferential for quasiconvex functions by using Penot and Volle's theorem. …

    Nonlinear Analysis : Theory, Methods & Applications 74(4), 1279-1285, 2011-02-15

    IR 

  • Set containment characterization and mathematical programming

    Suzuki Satoshi , Kuroiwa Daishi

    … In this paper, we introduce some set containment characterizations for quasiconvex programming. … Furthermore, we show a duality theorem for quasiconvex programming by using set containment characterizations. … Notions of quasiconjugate for quasiconvex functions, especially 1, -1-quasiconjugate, 1-semiconjugate, H-quasiconjugate and R-quasiconjugate, play important roles to derive characterizations of the set containments. …

    Proceedings : Fifth International Workshop on Computational Intelligence & Applications 2009(1), 264-266, 2009-11-11

    IR 

  • Set Containment Characterization and Mathematical Programming

    Suzuki Satoshi , Kuroiwa Daishi

    … In this paper, we introduce some set containment characterizations for quasiconvex programming. … Furthermore, we show a duality theorem for quasiconvex programming by using set containment characterizations. … Notions of quasiconjugate for quasiconvex functions, especially 1, -1-quasiconjugate, 1-semiconjugate, H-quasiconjugate and R-quasiconjugate, play important roles to derive characterizations of the set containments. …

    5th International Workshop on Computational Intelligence & Applications Proceedings : IWCIA 2009, 264-266, 2009-11

    IR 

  • Robustness Analysis of Trusses under Structural and Load Uncertainties

    Kanno Yoshihiro , Takewaki Izuru

    不確定なパラメータを有する構造物の挙動を把握するために,近年,構造物のロバスト性を評価するための種々の概念や手法が注目を集めている.本稿では,トラスの部材剛性および静的外力がインフォ・ギャップモデルに基づく不確定性を有することを仮定する.次に,トラスが有するロバスト性の指標として,変位の多項式で表される制約条件に関するロバストネス関数を定義する.さらに,ロバストネス関数の下解を与える準凸計画問題を …

    NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan 55(0), 53-53, 2006

    J-STAGE 

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