Second-order KarushKuhnTucker optimality conditions for set-valued optimization
In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the well-known Lagrange multiplier rule and the KurcyuszRobinsonZowe regularity assumption to a constrained set-valued optimization problem in the second-order case. Simultaneously, we also establish some second-order KarushKuhnTucker necessary and sufficient optimality conditions for a set-valued optimization problem, whose feasible set is determined by a set-valued map, under a generalized second-order KurcyuszRobinsonZowe regularity assumption.
optimality conditions set-valued optimization second-order composed contingent derivative lagrange multiplier rule regularity assumption karushkuhntucker condition 49j53 49k30 90c29 90c46