An approach to characterizing ε-solution sets of convex programs

被引：0

作者：

Tuyen, N., V ^{[1
]}

Wen, C-F ^{[2
,3
,4
]}

Son, T. Q. ^{[5
]}

机构：

[1] Hanoi Pedag Univ 2, Dept Math, Phuc Yen, Vinh Phuc, Vietnam

[2] Kaohsiung Med Univ, Ctr Fundamental Sci, Gaoxiong 80708, Taiwan

[3] Kaohsiung Med Univ, Res Ctr Nonlinear Anal & Optimizat, Gaoxiong 80708, Taiwan

[4] Kaohsiung Med Univ Hosp, Dept Med Res, Gaoxiong 80708, Taiwan

[5] Saigon Univ, Fac Math & Applicat, Ho Chi Minh City, Vietnam

来源：

TOP | 2022年 / 30卷 / 02期

关键词：

epsilon-solution; epsilon-solution set; Minimizing sequence; epsilon-Kuhn-Tucker vector; OPTIMALITY CONDITIONS; INFINITE NUMBER; DUALITY;

D O I：

10.1007/s11750-021-00616-y

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, we propose an approach to characterizing epsilon-solution sets of convex programs with a given epsilon > 0. The results are divided into two parts. The first one is devoted to establishing the expressions of epsilon-solution sets of a class of convex infinite programs. The representation is given based on the study of relationships among the following three sets: the set of Lagrange multipliers corresponding to a given epsilon-solution, the set of epsilon-solutions of the dual problem corresponding, and the set of epsilon-Kuhn-Tucker vectors associated with the problem in consideration. The second one is devoted to some special cases: the epsilon-solution sets of convex programs that have set constraints and the almost epsilon-solution sets of convex programs that have finite convex constraints. Several examples are given.

引用

页码：249 / 269

页数：21

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