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
作者：丘小玲(贵州大学数学与统计学院)；彭定涛(贵州大学数学与统计学院)；贾文生(贵州大学科学技术研究院)
Author：QIU Xiao-Ling(School of Mathematics and Computer Science, Guizhou University)；PENG Ding-Tao(School of Mathematics and Computer Science, Guizhou University)；JIA Wen-Sheng(Institute of Science and Technology, Guizhou University)
收稿日期：2016-08-11 年卷（期）页码：2017,54(2):239-248
期刊名称：四川大学学报: 自然科学版
Journal Name：Journal of Sichuan University (Natural Science Edition)
关键字：平衡问题; 非凸性; usco映射; 通有唯一性; 通有良定性
Key words：equilibrium problem; nonconvexity; usco mapping; generic uniqueness; generic well-posedness
基金项目：
中文摘要
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.
英文摘要
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.
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