A Note on Pointwise Well-Posedness of Set-Valued Optimization Problems

Kuntal Som and Vellaichamy Vetrivel
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Kuntal Som: Indian Institute of Technology Madras
Vellaichamy Vetrivel: Indian Institute of Technology Madras

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 2, No 9, 628-647

Abstract: Abstract Well-posedness for optimization problems is a well-known notion and has been studied extensively for scalar, vector, and set-valued optimization problems. For the set-valued case, there are many subdivisions: firstly in terms of pointwise notion and global notion and secondly in terms of the solution concepts, like the vector approach, the set-relation approach, etc. Various definitions of pointwise well-posedness for a set-valued optimization problem in the set-relation approach have been proposed in the literature. Here we do a comparative study and suggest modifications in some existing results. We also introduce a new pointwise well-posedness and discuss its properties and connection with others.

Keywords: Set-valued optimization; Well-posedness; Upper continuity; Pointwise well-posedness; Scalarization; Approximate solution set-valued map (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01981-1

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