一类广义凸集值映射优化问题弱有效解的最优性条件

The Optimality Conditions of Weak Efficient Solutions for the Optimization Problem of a Class of Generalized Convex Set-valued Mapping

在拓扑向量空间中定义了(u,0V)-广义次似凸集值映射.在相对内部的条件下,利用凸集分离定理,建立了此映射的择一定理.利用此择一定理,获得了带广义等式和不等式约束的优化问题的弱有效解的最优性条件.

In this paper, the concept of （u ,0v）-generalized subconvexlike map is defined in topological vector spaces. Under the relative interior, the alternative theorem of the map is estabished by the convex set separation theorem. Finally, using the altenative theorem, the optimality conditions of weak efficient solutions for the optimization problem with generalized equality and inequality constraints are obtained.