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

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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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Acknowledgements

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.

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  1. Department of Mathematics, University of Delhi South Campus, Benito Juarez Road, New Delhi, 110 021, India

    Pradeep Kumar Sharma & C. S. Lalitha

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  1. Pradeep Kumar Sharma
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  2. C. S. Lalitha
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Correspondence to C. S. Lalitha.

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Sharma, P.K., Lalitha, C.S. Connectedness of the solution sets in generalized semi-infinite set optimization. Optim Lett 17, 1575–1594 (2023). https://doi.org/10.1007/s11590-022-01943-0

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