线性空间中向量均衡问题解的最优性条件

Optimality conditions for vector equilibrium problems in linear spaces

研究了带约束的向量均衡问题的最优性条件,获得了线性空间中向量均衡问题的弱有效解的充分条件、必要条件及局部凸空间中向量均衡问题的有效解的必要条件,并给出了向量变分不等式的弱有效解的充要条件.从而将向量均衡问题的解的最优性条件从拓扑空间推广到线性空间.

The optimality conditions of the vector equilibrium problems with constraints in linear spaces were studied. It was obtained the sufficient condition and necessary condition for weakly efficient solution of the vector equilibrium problems in the linear space and the necessary condition for efficient solution of the vector equilibrium problems in locally convex spaces. Furthermore,the sufficient and necessary conditions for weakly efficient solution to the vector variational inequality problem was also given. Theroefore,it was presented the optimality conditions extended from the topological spaces to the linear spaces.