Convergence of the solution sets for set optimization problems

Ansari, Qamrul Hasan, Hussain, Nasir and Sharma, Pradeep Kumar (2022) Convergence of the solution sets for set optimization problems. Journal of Nonlinear and Variational Analysis, 6 (3), 165-183. (doi:10.23952/JNVA.6.2022.3.01).

Record type: Article

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.

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JNVA2022-3-1-2

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e-pub ahead of print date: 1 June 2022

Additional Information: Funding Information: The second author was supported by CSIR-UGC Junior Research Fellowship, India, Human Resource Development Group (Ref. No. 19/06/2016(i)EU-V), while third author was supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship No. F.42/2006 (BSR)/MA/19-20/0040.

Keywords: Locally lipschitz continuity, Painlevé-Kuratowski convergence, Set optimization problems, Set relations