Existence of Solutions of Bifunction-Set Optimization Problems in Metric Spaces

Pham Huu Sach () and Le Anh Tuan
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Pham Huu Sach: Vietnam Academy of Science and Technology
Le Anh Tuan: Nong Lam University

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 1, No 8, 195-225

Abstract: Abstract Sufficient conditions are given for the existence of solutions of bifunction-set optimization problems, whose underlying sets are complete metric spaces. The main result of this paper is formulated in Theorem 3.1, with the help of some new data. The advantage of introducing the new data is that, by choosing suitable new data, we can obtain existence results with assumptions, that are imposed directly on the objective maps, or that are formulated via scalarization. The main result is applied successfully to Kuroiwa set optimization problems and Ky Fan vector inequality problems. We also discuss equivalences between the existence of solutions of the bifunction-set optimization problem, an Ekeland-type variational principle and a Caristi-type fixed point theorem. Examples are provided.

Keywords: Bifunction-set optimization; Set optimization; Ky Fan inequality; Set-valued map; Solution existence; Metric space; 49J27; 49K27; 90C29 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01958-0

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