A Generalized Alternative Theorem of Partial and Generalized Cone Subconvexlike Set-Valued Maps and Its Applications in Linear Spaces

Abstract EN

We first introduce a new notion of the partial and generalized cone subconvexlike set-valued map and give an equivalent characterization of the partial and generalized cone subconvexlike set-valued map in linear spaces.

Secondly, a generalized alternative theorem of the partial and generalized cone subconvexlike set-valued map was presented.

Finally, Kuhn-Tucker conditions of set-valued optimization problems were established in the sense of globally proper efficiency.