一类平衡问题的通有唯一性与良定性

Generic Uniqueness and Generic Well-posedness on a class of Equilibrium Problems

摘要:

本文首先构造没有凸性的平衡问题空间, 以集值映射为工具, 在紧值和非紧集的环境下, 证明了平衡问题的解是通有唯一的, 也就是说, 在Baire分类的意义下, 大多数的平衡问题都有唯一解. 然后, 借助有限理性模型统一研究良定性的方法, 也得到平衡问题的解是通有良定的.最后, 给出了平衡问题解的刻画定理.

Abstract:

It is first constructed the spaces of the equilibrium problems with nonconvexity in compact or noncompact setting via the set-valued mapping, and proved the equilibrium problems possess generic unique properties that means, in the sense of Baire category, most equilibrium problems have unique solution. Then it is also obtained generic well-posedness on equilibrium problem by virtue of bounded rational model of unified the well-posedness. The characteristic expression theorems of the solutions are given at last.