本文研究集值优化问题在严有效意义下的鞍点理论及对偶理论。首先,给出集值优化问题在严有效意义下鞍点的一个等价命题和鞍点定理。其次,在某种凸性假设下,研究严有效意义下鞍点最优性条件、弱对偶性、强对偶性、逆对偶性。
This paper studies the saddle point and duality theory of set-valued optimization problems in the sense of strict efficiency. An equavilent proposition of saddle point and a saddle point theorem in the sense of strict efficiency are given. The optimality conditions of saddle points, weakly duality theorem, strong duality theorem and converse duality theorem are obtained under convexity assumptions.