Kuhn-Tucker Optimality Conditions for Set-Valued Optimization Problem in the Sense of Strongly Efficient Solutions

Abstract:

      Kuhn-Tucker optimality conditions for the set-valued optimization problem (VP) with constraints are considered in the sense of strongly efficient solutions in locally convex spaces. Under the assumption of nearly cone-subconvexlikeness, by applying alternative theorem, a Kuhn-Tucker optimality necessary condition for (VP) is derived. By using the properties of base functionals, a sufficient condition is also obtained. Finally, a kind of unconstrained program equivalent to (VP) is established.