Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation

被引：29

作者：

Lam Quoc Anh ^{[1
]}

Tran Quoc Duy ^{[2
,3
]}

Dinh Vinh Hien ^{[4
,5
]}

Kuroiwa, Daishi ^{[6
]}

Petrot, Narin ^{[7
]}

机构：

[1] Cantho Univ, Dept Math, Teacher Coll, Can Tho, Vietnam

[2] Ton Duc Thang Univ, Div Computat Math & Engn, Inst Computat Sci, Ho Chi Minh City, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[4] Vietnam Natl Univ Ho Chi Minh City, Univ Sci, Fac Math & Comp Sci, Ho Chi Minh City, Vietnam

[5] Ho Chi Minh City Univ Food Ind, Dept Math, Ho Chi Minh City, Vietnam

[6] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

[7] Naresuan Univ, Fac Sci, Dept Math, Phitsanulok 65000, Thailand

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2020年 / 185卷 / 02期

关键词：

Set optimization; Set less order relation; Internal stability; External stability; WELL-POSEDNESS; SCALARIZATION; POINTWISE; STABILITY;

D O I：

10.1007/s10957-020-01657-2

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：

This article investigates stability conditions for set optimization problems with the set less order relation in the senses of Panileve-Kuratowski and Hausdorff convergence. Properties of various kinds of convergences for elements in the image space are discussed. Taking such properties into account, formulations of internal and external stability of the solutions are studied in the image space in terms of the convergence of a solution sets sequence of perturbed set optimization problems to a solution set of the given problem.

引用

页码：416 / 432

页数：17

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