New Second-Order Tangent Epiderivatives and Applications to Set-Valued Optimization

Abstract

A new second-order tangent set is introduced, with which a new second-order tangent epiderivative is also introduced for a set-valued map. Applying a separation theorem for convex sets, second-order Fritz John and Kuhn---Tucker necessary optimality conditions are obtained for a point pair to be a weak minimizer of set-valued optimization problem. Under the assumption of lower semicontinuous, a second-order Kuhn---Tucker sufficient optimality condition is obtained for a point pair to be a weak minimizer of set-valued optimization problem.