CONVERGENCE OF THE SOLUTION SETS FOR SET OPTIMIZATION PROBLEMS

Qamrul Hasan Ansari; Nasir Hussain; Pradeep Kumar Sharma

doi:10.23952/JNVA.6.2022.3.01

CONVERGENCE OF THE SOLUTION SETS FOR SET OPTIMIZATION PROBLEMS

Qamrul Hasan Ansari^*
, Nasir Hussain
, Pradeep Kumar Sharma

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this paper, we present the stability analysis of solution sets for set optimization problems with respect to the set order relation defined by means of Minkowski difference. We introduce the concepts of weak/weak^# locally Lipschitz continuity and the concepts of ml-quasiconnectedness and strictly ml-quasiconnectedness for set-valued mappings. By using these concepts, we study the Painlevé-Kuratowski convergence of the solution sets for perturbed set optimization problems. Several examples are given to illustrate our results.

Original language	English
Pages (from-to)	165-183
Number of pages	19
Journal	Journal of Nonlinear and Variational Analysis
Volume	6
Issue number	3
DOIs	https://doi.org/10.23952/JNVA.6.2022.3.01
State	Published - 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 Journal of Nonlinear and Variational Analysis

Keywords

Locally lipschitz continuity
Painlevé-Kuratowski convergence
Set optimization problems
Set relations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.23952/JNVA.6.2022.3.01

Cite this

@article{174e601197794959839c99bc4ea47770,

title = "CONVERGENCE OF THE SOLUTION SETS FOR SET OPTIMIZATION PROBLEMS",

abstract = "In this paper, we present the stability analysis of solution sets for set optimization problems with respect to the set order relation defined by means of Minkowski difference. We introduce the concepts of weak/weak\# locally Lipschitz continuity and the concepts of ml-quasiconnectedness and strictly ml-quasiconnectedness for set-valued mappings. By using these concepts, we study the Painlev{\'e}-Kuratowski convergence of the solution sets for perturbed set optimization problems. Several examples are given to illustrate our results.",

keywords = "Locally lipschitz continuity, Painlev{\'e}-Kuratowski convergence, Set optimization problems, Set relations",

author = "Ansari, \{Qamrul Hasan\} and Nasir Hussain and Sharma, \{Pradeep Kumar\}",

note = "Publisher Copyright: {\textcopyright} 2022 Journal of Nonlinear and Variational Analysis",

year = "2022",

doi = "10.23952/JNVA.6.2022.3.01",

language = "English",

volume = "6",

pages = "165--183",

journal = "Journal of Nonlinear and Variational Analysis",

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T1 - CONVERGENCE OF THE SOLUTION SETS FOR SET OPTIMIZATION PROBLEMS

AU - Ansari, Qamrul Hasan

AU - Hussain, Nasir

AU - Sharma, Pradeep Kumar

PY - 2022

Y1 - 2022

N2 - In this paper, we present the stability analysis of solution sets for set optimization problems with respect to the set order relation defined by means of Minkowski difference. We introduce the concepts of weak/weak# locally Lipschitz continuity and the concepts of ml-quasiconnectedness and strictly ml-quasiconnectedness for set-valued mappings. By using these concepts, we study the Painlevé-Kuratowski convergence of the solution sets for perturbed set optimization problems. Several examples are given to illustrate our results.

AB - In this paper, we present the stability analysis of solution sets for set optimization problems with respect to the set order relation defined by means of Minkowski difference. We introduce the concepts of weak/weak# locally Lipschitz continuity and the concepts of ml-quasiconnectedness and strictly ml-quasiconnectedness for set-valued mappings. By using these concepts, we study the Painlevé-Kuratowski convergence of the solution sets for perturbed set optimization problems. Several examples are given to illustrate our results.

KW - Locally lipschitz continuity

KW - Painlevé-Kuratowski convergence

KW - Set optimization problems

KW - Set relations

UR - https://www.scopus.com/pages/publications/85130697831

U2 - 10.23952/JNVA.6.2022.3.01

DO - 10.23952/JNVA.6.2022.3.01

M3 - Article

AN - SCOPUS:85130697831

SN - 2560-6921

VL - 6

SP - 165

EP - 183

JO - Journal of Nonlinear and Variational Analysis

JF - Journal of Nonlinear and Variational Analysis

IS - 3

ER -

CONVERGENCE OF THE SOLUTION SETS FOR SET OPTIMIZATION PROBLEMS

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this