External and internal stability in set optimization using gamma convergence

被引：1

作者：

Karuna ^{[1
]}

Lalitha, C. S.

机构：

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

来源：

CARPATHIAN JOURNAL OF MATHEMATICS | 2019年 / 35卷 / 03期

关键词：

Painleve-Kuratowski convergence; Gamma-convergence; domination property; stability; set optimization; WELL-POSEDNESS; SCALARIZATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main objective of this paper is to investigate the stability of solution sets of perturbed set optimization problems in the decision space as well as in the image space, by perturbing the objective maps. For a sequence of set-valued maps, a notion of gamma convergence is introduced to establish the external and internal stability in terms of Painleve-Kuratowski convergence of sequence of solution sets of perturbed problems under certain compactness assumptions and domination properties.

引用

页码：393 / 406

页数：14

共 50 条

[41] On the Stability of the Boundary of the Feasible Set in Linear Optimization [J].

Miguel A. Goberna ;

Mercedes Larriqueta ;

Virginia N. Vera de Serio .

Set-Valued Analysis, 2003, 11 :203-223

[42] The stability of minimal solution sets for set optimization problems via improvement sets [J].

Li, Taiyong ;

Wei, Yanhui .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2023, 2023 (01)

[43] Analysis of optimization algorithms for stability and convergence for natural language processing using deep learning algorithms [J].

Gangadhar C. ;

Moutteyan M. ;

Vallabhuni R.R. ;

Vijayan V.P. ;

Sharma N. ;

Theivadas R. .

Measurement: Sensors, 2023, 27

[44] SCALARIZATION AND WELL-POSEDNESS FOR SET OPTIMIZATION PROBLEMS USING GENERALIZED ORIENTED DISTANCE FUNCTION [J].

Li, TaiYong ;

Xu, GuangHui .

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2025, 21 (02) :1584-1599

[45] Approximate Solutions and Levitin–Polyak Well-Posedness for Set Optimization Using Weak Efficiency [J].

Meenakshi Gupta ;

Manjari Srivastava .

Journal of Optimization Theory and Applications, 2020, 186 :191-208

[46] Stability of minimal solutions to parametric set optimization problems [J].

Khoshkhabar-amiranloo, S. .

APPLICABLE ANALYSIS, 2018, 97 (14) :2510-2522

[47] Stability of solutions for fuzzy set optimization problems with applications [J].

Zhang, Chuang-liang ;

Huang, Nan-jing ;

O'Regan, Donal .

FUZZY SETS AND SYSTEMS, 2023, 466

[48] On the Stability of the Optimal Value and the Optimal Set in Optimization Problems [J].

Dinh, N. ;

Goberna, M. A. ;

Lopez, M. A. .

JOURNAL OF CONVEX ANALYSIS, 2012, 19 (04) :927-953

[49] INTERNAL AND EXTERNAL STABILITY AND ROBUST STABILITY CONDITION FOR A CLASS OF INFINITE-DIMENSIONAL SYSTEMS [J].

YAMAMOTO, Y ;

HARA, S .

AUTOMATICA, 1992, 28 (01) :81-93

[50] Scalarizations for a set optimization problem using generalized oriented distance function [J].

C. S. Khushboo .

Positivity, 2019, 23 :1195-1213

← 1 2 3 4 5 →