Abstract:

By applying properties of the nearly cone-subconvexlike setvalued map, the result was proved that for a nearly cone-subconvexlike ordered pair set-valued map, its relevant Lagrange map is also nearly cone-subconvexlike. With help of such result, a Lagrange optimality necessary condition was established in the sense of  ε-strongly efficiency. By taking advantage of properties of an  ε-strongly efficient point, a Lagrange optimality sufficient condition was  also obtained.

Key words: ε-strongly efficient element; near cone-subconvexlikeness; set-valued optimization