Kuhn-tucker condition and wolfe duality of preinvex set-valued optimization

Abstract

The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.

Set-valued optimization problems via second-order contingent epiderivative

“…It is an extension of the notion of directional derivative to the set-valued case. Sheng and Liu [22] investigated the KKT conditions of set-valued optimization problems via generalized contingent epiderivative and preinvexity assumptions. Rodríguez-Marín and Sama [21] investigated the existence, uniqueness, and properties of contingent epiderivative.…”