Contractibility of the solution sets for set optimization problems. (English) Zbl 07923316
Summary: This paper aims at investigating the contractibility of the solution sets for set optimization problems by utilizing strictly quasi cone-convexlikeness, which is an assumption weaker than strictly cone-convexity, strictly cone-quasiconvexity, and strictly naturally quasi cone-convexity. We establish the contractibility of \(l\)-minimal, \(l\)-weak minimal, \(u\)-minimal, and \(u\)-weak minimal solution sets for set optimization problems by using the star-shape sets and the nonlinear scalarizing functions for sets. Moreover, we also discuss the arcwise connectedness and the contractibility of \(p\)-minimal and \(p\)-weak minimal solution sets for set optimization problems by using the scalarization technique. Finally, our main results are applied to the contractibility of the solution sets for vector optimization problems.
Keywords:
contractibility; nonlinear scalarizing function; set optimization problems; strictly quasi cone-convexlikenessReferences:
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