Levitin-polyak well-posedness for set optimization problems

Ansart, Qamrul Hasan, Hussain, Nasir and Sharma, Pradeep Kumar (2021) Levitin-polyak well-posedness for set optimization problems. Journal of Nonlinear and Convex Analysis, 22 (7), 1353-1371.

Record type: Article

Abstract

In this paper, we study different kinds of Levitin-Polyak well-posedness for set optimization problems and their relationships with respect to the set order relations defined by Minkowski difference on the family of bounded sets. Furthermore, by using the Kuratowski measure of noncompactness, we give some characterizations of Levitin-Polyak well-posedness for set optimization problems. Moreover, we establish the relationship between stability and LP well-posedness of set optimization problem by defining approximating solution maps. Several examples are given in support of concepts and results of this paper.

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Published date: July 2021

Additional Information: Funding Information: this research, first author was supported by DST-SERB Project No. MTR/2017/000135. Second author was supported by CSIR-UGC, Junior Research Fellowship, India, Human Resource Development Group (Ref. No. 19/06/2016(i)EU-V).. Third author was supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship No. F.4-2/2006 (BSR)/MA/19-20/0040.

Keywords: Levitin-Polyak well-posedness, Set optimization problems, Set order relations, Stability