Abstract: 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.

Key words: strictly maximal efficient solution, mth-order contingent derivative, set-valued optimization