Search Results 1-16 of 16

  • Duality Theorems for Convex and Quasiconvex Set Functions

    Suzuki Satoshi , Kuroiwa Daishi

    … 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. … In this paper, we study duality theorems for convex and quasiconvex set functions. … We show Lagrange duality theorem for convex set functions and surrogate duality theorem for quasiconvex set functions under the Slater condition. …

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

    IR 

  • Optimality Conditions and Constraint Qualifications for Quasiconvex Programming

    Suzuki Satoshi

    … Recently, by using Greenberg–Pierskalla subdifferential and Martínez-Legaz subdifferential, necessary and sufficient optimality conditions for quasiconvex programming have been introduced. … In this paper, we study optimality conditions and constraint qualifications for quasiconvex programming. … Additionally, we show some equivalence relations between duality results for convex and quasiconvex programming. …

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

    IR 

  • Nonlinear error bounds for quasiconvex inequality systems

    Suzuki Satoshi , Kuroiwa Daishi

    … The error bound is an inequality that restricts the distance from a vector to a given set by a residual function. … For quasiconvex inequality systems, there are so many examples such that systems do not have Lipschitzian and Holderian error bounds. … However, the research of nonlinear error bounds for quasiconvex inequality systems have not been investigated yet as far as we know. … In this paper, we study nonlinear error bounds for quasiconvex inequality systems. …

    Optimization letters 11(1), 107-120, 2017-01

    IR 

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

    Suzuki Satoshi , Kuroiwa Daishi

    … An invariance property of the subdifferential of the objective function is studied, and as a consequence, characterizations of the solution set by any solution point and any point in the relative interior of the solution set are given. …

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

    IR 

  • Necessary and Sufficient Constraint Qualification for Surrogate Duality

    Suzuki Satoshi , Kuroiwa Daishi

    … Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. …

    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. … Especially, we show results of a chain rule for composition with non-decreasing functions, monotonicity of the Qsubdifferential, mean-value theorem, a sufficient condition for a global minimizer for quasiconvex programming, and the calculus of the Q-subdifferential of the supremum 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 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 

  • Characterizing set containments with quasiconvex inequalities (Nonlinear analysis and convex analysis)

    SUZUKI SATOSHI , KUROIWA DAISHI

    RIMS Kokyuroku (1611), 56-60, 2008-09

    IR 

  • A Note on Discrete Convexity and Local Optimality

    UI Takashi

    … One of the most important properties of a convex function is that a local optimum is also a global optimum. … We consider arbitrary locality in a discrete space and the corresponding local optimum of a function over the discrete space. … We introduce the corresponding notion of discrete convexity and show that the local optimum of a function satisfying the discrete convexity is also a global optimum. …

    Japan Journal of Industrial and Applied Mathematics 23(1), 21-29, 2006-02-01

    IR  References (14)

  • 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 

  • APPROXIMATION ALGORITHM FOR ROBUSTNESS FUNCTIONS OF TRUSSES WITH UNCERTAIN STIFFNESS UNDER UNCERTAIN FORCES  [in Japanese]

    KANNO Yoshihiro , TAKEWAKI Izuru

    … Under the uncertainties of member stiffness and external forces based on the info-gap model, the robustness function is formulated as the optimal objective value of an optimization problem with infinitely many constraint conditions. … By using the semidefinite programming relaxation, we formulate the quasiconvex programming problem which provides the lower bounds of the robustness functions. …

    Journal of Structural and Construction Engineering (Transactions of AIJ) 70(591), 53-60, 2005

    J-STAGE  AIJ  References (29)

  • Quasi M-convex Functions and Minimization Algorithms (Algorithm Engineering as a New Paradigm)

    Murota Kazuo , Shioura Akiyoshi

    RIMS Kokyuroku (1185), 150-159, 2001-01

    IR 

  • An Algorithm for Seeking a Global Minimal Value of 2-Dimensional Multimodal Functions  [in Japanese]

    KANEMITSU Hideo , SHIMBO Masaru

    複数の孤立極小点を矩形探索領域にもつ二変数多峰性関数の最小値を探索するアルゴリズムを提案する.本稿では,各極点に対する強準凸領域を新たに定義し4隣接格子が極小点を囲むための条件を導く.さらに,この領域の極小点の近傍で,「正定値二次形式で近似でき,その主軸が座標軸と平行」を仮定したときに,極小点を囲むための条件として,中心点とその隣接格子点て成立する関数値間の関係を導く.次に,この関係を用いて,4つ …

    IPSJ SIG Notes 1, 41-48, 1995-05-18

    References (7)

  • DEMAND FOR DIFFERENTIATED BRANDS, ADVERTISING AND RD ACTIVITY

    KAWASHIMA Yasuo

    … A quasiconvex utility function is introduced to deal with demand for brands. …

    Keio economic studies 22(2), 35-50, 1985

    IR 

Page Top