Generalized Higher-Order Optimality Condition For Super Efficient Solutions Of Set-valued Optimization

The super efficient solution of set-valued optimization is considered in real normed spaces. For a specific set, its super efficient points set is obtained by direct calculation. Without any convexity assumption, by employing Henig dilating cone, generalized higher-order derivative necessary condition is established for set-valued optimization problem to attain its super efficient solutions. a generalized higher-order cone-directed contingent (adjacent) derivative for a set-valued map are introduced, and generalized higher-order necessary and sufficient conditions are obtained for a set-valued optimization Problem.and cone-directed higher order generalized tangent derivatives to study the set-value of the constrained optimization problem of the higher order duality.