含参集值弱平衡问题解集映射的下半连续性

On the Lower Semicontinuity of the Solution Set Map to Parametric Set-Valued Weak Equilibrium Problems

含参变分不等式或含参向量平衡问题解集映射的稳定性分析是向量优化理论的研究热点之一.在不需要单调性及任何解集信息的假设条件下,利用标量化的方法和一个下半连续集值映射簇的并仍然是下半连续的性质,在实Huasdorff拓扑向量空间中得到了含参集值弱向量平衡问题解集映射下半连续性的一个充分性条件.证明中所用的标量化解(f-有效解)集不必是单值的,可以是一般集合.这些结果推广或改进了已有文献的一些结果,并通过例子说明了所得结果的正确性.

The stability analysis of the solution mappings for parametric vector variational inequalities and parametric vector equilibrium problems is one of focus in vector optimization theory.In this paper,by using scalarization method and a property that the union of a family of lower semicontinuous set-valued mappings is also lower semicontinuous,we obtain a sufficient condition for the lower semicontinuity of the solution mappings to parametric set-valued weak vector equilibrium problems in real Hausdorff topological vector spaces,where the assumption of monotonicity and any information about the solution set are not necessary.The scalafization （f-effi-cient） solution set in the proof may be a general set in our paper,but not a singleton.These results extend and improve the recent ones in the literature.Some examples are given to illustrate the correctness of our results.