集值优化问题超鞍点的最优性条件

Optimality Conditions for Super Saddle Points of Set-valued Optimizition

在Hausdorff局部凸拓扑线性空间中,利用Lagrange集值映射,对集值优化问题(SOP),引进了集值映射超鞍点的概念.利用凸集分离定理证明了两个标量化引理,并得到了超鞍点定理和超鞍点的等价刻画定理,从而解决了用超鞍点刻画超有效性的问题.

In Hausdorff locally convex spaces, the concept of super saddle points of a set-valued map is introduced by means of Lagrange set-valued map for the set-valued vector optimization problem （SOP）. Two sealarization lemmas are proved, and the theorem of super saddle points and the equivalent characterization of super saddle points are obtained by the separation theorem of convex sets. Therefore the issues charactering super efficiency by super saddle points are solved.