含参原始与对偶弱向量近似平衡问题的稳定性

The Stability of Parametric Primal and Dual Weak Vector Approximate Equilibrium Problems

借助于标量化技巧讨论了含参原始与对偶弱向量近似平衡问题的稳定性.首先,在邻近C-次似凸性假设下获得原始平衡问题近似解集的连通性和近似解集映射的Hausdorff上(下)半连续性.然后,利用标量化方法,在较弱假设下获得了含参对偶弱向量平衡问题近似解集的连通性及近似解集映射的Hausdorff连续性的充分性条件.最后,给出了在向量优化问题中的一个应用.所得结果推广和改进了已有文献中相应结论.

In this paper, we discuss the stability of parametric primal and dual weak vector approximate equilibrium problems under the scalarization method. Firstly, the connectedness of approximate solutions set and the Hausdorff upper （lower） semi- continuity of approximate solution mappings to parametric primal weak equilibrium problems, under the assumption of nearly C-subcovexlikeness, are obtained. Then,under some weak assumptions, some su^cient conditions of the connectedness of approximate solutions set and the Hausdorff continuity of approximate solution map- pings to parametric dual weak vector equilibrium problems are obtained, by using the scalarization method. At last, an application in vector optimization problems is given. The obtained results improve and generalize the corresponding ones in the literature