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This paper aims at investigating the contractibility of the solution sets forset optimization problems by utilizing strictly quasi cone-convexlikeness,which is an assumption weaker than strictly cone-convexity, strictlycone-quasiconvexity and strictly naturally quasi cone-convexity. We establishthe contractibility of l-minimal, l-weak minimal, u-minimal and u-weak minimalsolution sets for set optimization problems by using the star-shape sets andthe nonlinear scalarizing functions for sets. Moreover, we also discuss thearcwise connectedness and the contractibility of p-minimal and p-weak minimalsolution sets for set optimization problems by using the scalarizationtechnique. Finally, our main results are applied to the contractibility of thesolution sets for vector optimization problems.

Contractibility of the solution sets for set optimization problems