Existence and connectedness of the l-minimal approximate solutions for set optimization problems: an application in generalized multiobjective robustness
The Journal of Analysis - Trang 1-26 - 2023
Tóm tắt
The goal of this paper is to study the existence and connectedness of the l-minimal approximate solutions of the set-valued optimization problem using an extended signed distance function. The existence of the l-minimal approximate solutions is established by virtue of the FAN-KKM and Cantor’s intersection theorems. A scalarization result of the set of l-minimal approximate solutions is proposed without adopting the convexity notion of the objective function. By using this scalarization result, we explore the (path) connectedness of the l-minimal approximate solutions. Moreover, we apply our approach to generalized multiobjective robustness problems. Some necessary examples are illustrated to validate our main results.
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