Optimality Conditions For Set-Valued Optimization On Strictly Efficient Solutions

The strict efficiency of set-valued optimization is considered in real normed spaces.When both objective function and constraint function are concave, with higher-order derivatives by applying separation theorem for convex sets, Fritz John type necessary optimality condition is established for set-valued optimization problem with constraint to attain its strict maximal solution. With the properties of base functional by applying the constructive method, sufficient optimality condition is also derived. And the strict efficiency of set-valued optimization is considered in real normed spaces. By applying the properties of higher-order derivatives, higher-order type necessary optimality condition is established for a set-valued optimization problem whose constraint condition is determined by a fixed set to attain its strictly maximal efficient solution. When objective function is concave, with the properties of strictly maximal efficient point, sufficient optimality condition is also derived.