Convergence, Scalarization and Continuity of Minimal Solutions in Set Optimization

被引：1

作者：

Karuna ^{[1
]}

Lalitha, C. S. ^{[2
]}

机构：

[1] Univ Delhi, Dept Math, Delhi 110007, India

[2] Univ Delhi, Dept Math, South Campus, Delhi 110021, India

来源：

JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA | 2024年 / 12卷 / 03期

关键词：

Topological convergence; Painleve-Kuratowski convergence; Upper semicontinuity; Lower semicontinuity; Stability; Scalarization; WELL-POSEDNESS; STABILITY;

D O I：

10.1007/s40305-022-00440-6

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：

The paper deals with the study of two different aspects of stability in the given space as well as the image space, where the solution concepts are based on a partial order relation on the family of bounded subsets of a real normed linear space. The first aspect of stability deals with the topological set convergence of families of solution sets of perturbed problems in the image space and Painleve-Kuratowski set convergence of solution sets of the perturbed problems in the given space. The convergence in the given space is also established in terms of solution sets of scalarized perturbed problems. The second aspect of stability deals with semicontinuity of the solution set maps of parametric perturbed problems in both the spaces.

引用

页码：773 / 793

页数：21

共 30 条

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