Abstract: The properties of saddlepoint for scalar set valued Lagrange mapping in vector optimization problems with setvalued maps were studied. Under the assumption of nearly conesubconveslikeness, the sufficient and necessary conditions for a strict efficient solution being a saddlepoint in setvalued optimization problems are proposed. The strong and weak dual theorems are obtained in the sense of strictly efficiency in dual model which is established by scalar setvalued Lagrange mapping.

Key words: setvalued optimization, Lagrange mapping, saddle point, strictly efficiency, dual