Necessary optimality conditions for minimax programming problems with mathematical constraints

被引：4

作者：

Bao, Truong Q. ^{[1
]}

Gupta, Pankaj ^{[2
]}

Khanh, Phan Q. ^{[3
]}

机构：

[1] Northern Michigan Univ, Dept Math & Comp Sci, Marquette, MI 49855 USA

[2] Univ Delhi, Dept Operat Res, New Delhi, India

[3] Vietnam Natl Univ, Int Univ, Dept Math, Ho Chi Minh, Vietnam

来源：

OPTIMIZATION | 2017年 / 66卷 / 11期

关键词：

Minimax programming; upper subdifferential necessary optimality conditions; lower subdifferential necessary optimality conditions; fuzzy necessary optimality conditions; minimax fractional programming; EQUILIBRIUM CONSTRAINTS; SUBDIFFERENTIAL CALCULUS; OPTIMIZATION;

D O I：

10.1080/02331934.2017.1344238

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, necessary optimality conditions in terms of upper and/or lower subdifferentials of both cost and constraint functions are derived for minimax optimization problems with inequality, equality and geometric constraints in the setting of non-differentiatiable and non-Lipschitz functions in Asplund spaces. Necessary optimality conditions in the fuzzy form are also presented. An application of the fuzzy necessary optimality condition is shown by considering minimax fractional programming problem.

引用

页码：1755 / 1776

页数：22

共 14 条

[1] Necessary conditions in multiobjective optimization with equilibrium constraints [J].

Bao, T. Q. ;

Gupta, P. ;

Mordukhovich, B. S. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2007, 135 (02) :179-203

[2]

Bao TQ, 2007, FRECHET SUB IN PRESS

[3] Subdifferential necessary conditions in set-valued optimization problems with equilibrium constraints [J].

Bao, Truong Q. .

OPTIMIZATION, 2014, 63 (02) :181-205

[4] Relative Pareto minimizers for multiobjective problems: existence and optimality conditions [J].

Bao, Truong Q. ;

Mordukhovich, Boris S. .

MATHEMATICAL PROGRAMMING, 2010, 122 (02) :301-347

[5] SUBOPTIMALITY CONDITIONS FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS [J].

Bao, Truong Q. ;

Gupta, Pankaj ;

Mordulchovich, Boris S. .

TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (09) :2569-2592

[6]

Borwein J.M., 2005, CMS BOOKS MATH

[7] TANGENTIAL APPROXIMATIONS [J].

BORWEIN, JM ;

STROJWAS, HM .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1985, 9 (12) :1347-1366

[8] ALGORITHMS FOR GENERALIZED FRACTIONAL-PROGRAMMING [J].

CROUZEIX, JP ;

FERLAND, JA .

MATHEMATICAL PROGRAMMING, 1991, 52 (02) :191-207

[9] VARIATIONAL PRINCIPLE [J].

EKELAND, I .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 47 (02) :324-353

[10] Frechet subdifferential calculus and optimality conditions in nondifferentiable programming [J].

Mordukhovich, B. S. ;

Nam, N. M. ;

Yen, N. D. .

OPTIMIZATION, 2006, 55 (5-6) :685-708

← 1 2 →