具约束向量拟均衡问题的Global有效解的最优条件

Optimality conditions for the global efficient solution of vector quasi-equilibrium problems with constrians

向量均衡问题是运筹学的重要组成部分,其研究的主要内容包含各种解的存在性、稳定性、连续性、连通性、适定性、最优条件。向量均衡问题的解主要有有效解、弱有效解、强有效解、Global有效解、Henig有效解、超有效解。研究向量均衡问题各种有效解的最优条件是向量均衡问题的一个重要课题。首先,在实Hausdorff拓扑线性空间中引入具约束条件的向量拟均衡问题及其Global有效解的概念;其次,在实拓扑线性空间中分析了锥-凸、几乎锥-类凸与几乎锥-次类凸3种广义凸性的内在关系;最后,在3种广义凸性条件下借助于凸集分离定理给出了具约束条件的向量拟均衡问题Global有效解的充要条件。

Vector vector equilibrium problem is an important part of operations research,including the existence of various solutions,the stability of solutions,the continuity of solutions,the connectivity of solutions,the optimal conditions of solutions.The solution of vector equilibrium problem mainly contains effectivt solution,weak efficient solution,strong efficient solution,Global efficient solution,Henig efficient solution and super efficient solution.Studying optimal conditions of various efficient solutions of vector equilibrium problem is an important topic.Firstly,vector quasi-equilibrium problems with constrians and its Global efficient solution are introduced in real Hausdorff topological vector spaces.Secondly,the inner relations among cone convex,almost cone convex and almost conical sub-convex of generalized convexity are analyzed in real topological linear space.Finally,by using the separation of convex sets,under the generalized convexity conditions,the necessary and sufficient condtions for the Global efficient solution of vector quasiequilibrium problems with constrians are given.