Connectedness of the solution sets in generalized semi-infinite set optimization

Sharma, Pradeep Kumar and Lalitha, C.S. (2023) Connectedness of the solution sets in generalized semi-infinite set optimization. Optimization Letters, 17 (7), 1575-1594. (doi:10.1007/s11590-022-01943-0).

Record type: Article

Abstract

We first establish sufficient conditions for the arcwise connectedness of the image of the constraint set map and for the upper semi-continuity of the constraint set map. These results, together with scalarization techniques, are further used to establish the connectedness of the solution sets of generalized semi-infinite set optimization problems. An application to vector-valued game theory with uncertainty is given.

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More information

Accepted/In Press date: 6 October 2022

e-pub ahead of print date: 25 October 2022

Published date: September 2023

Additional Information: Funding Information: The authors are grateful to the handling editor and the anonymous referee for their valuable comments and suggestions, which helped to improve the previous draft of the paper. In this research, first author is supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship No. F.4-2/2006 (BSR)/MA/19-20/0040.

Keywords: Connectedness, Game theory, Oriented distance function, Semi-continuity, Set optimization