拓扑向量空间中向量极值问题的广义鞍点及对偶定理

Generalized Saddle Point and Duality Theorem of Vector Extremum Problems in Topological Vector Space

【目的】研究拓扑向量空间中向量极值问题的广义鞍点最优性条件及Lagrange对偶问题。【方法】引入拓扑向量空间中广义次似凸映射和择一定理,并以广义鞍点理论为分析基础。【结果】在刻画广义鞍点性质的基础上构建了拓扑空间中广义鞍点与向量极值问题弱Pareto最优解之间的关系及其对偶定理。【结论】理论分析结果表明向量极值问题的广义鞍点是弱Pareto最优解的必要不充分条件,给出了目标函数在其约束映射满足广义Slater约束规格条件下的Lagrange强、弱对偶定理。

[Purposes]The topological vector space is studied with vector extremum problems of generalized saddle point in the optimality conditions and lagrange dual problem.[Methods]The topological vector space is proposed in the generalized convex mapping and the theorem is chosen,and the properties of generalized saddle points are described.[Findings]The relationship is built between the topological space of generalized saddle points and the weak Paretooptimal solution of vector extremum problems and the Lagrange duality theorems.[Conclusions]The theoretical analysis results show that the generalized saddle point of vector extremum problem is a necessary and insufficient condition for the weak Pareto optimal solution,and the Lagrange strong and weak duality theorem of the objective function are given under the conditions of generalized Slater constraints..