运筹学学报 >
2025 , Vol. 29 >Issue 2: 201 - 213
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.02.016
广义弱混合向量拟平衡问题的逼近定理和通有收敛性
收稿日期: 2020-07-04
网络出版日期: 2025-06-12
基金资助
国家自然科学基金(12061020);国家自然科学基金(71961003);贵州省自然科学基金(20201Y284);贵州省自然科学基金(20205016);贵州省自然科学基金(2021088);贵州省自然科学基金(20215640)
版权
An approximation theorem and generic convergence for generalized weakly-mixed vector quasi-equilibrium problem
Received date: 2020-07-04
Online published: 2025-06-12
Copyright
本文研究广义弱混合向量拟平衡问题的逼近定理和通有收敛性。首先利用Fan-Knaster-Kuratowski-Mazurkiewicz (Fan-KKM) 引理给出了广义弱混合向量拟平衡问题解的存在性定理。然后基于Simon的有限理性理论, 在较弱的条件下给出了广义弱混合向量拟平衡问题的一个逼近定理。最后运用Fort定理, 证明了在Baire分类意义下广义弱混合向量拟平衡问题的解具有通有收敛的结果。
关键词： 广义弱混合向量拟平衡问题; Fan-KKM引理; 逼近定理; 通有收敛
冯旭东, 贾文生 . 广义弱混合向量拟平衡问题的逼近定理和通有收敛性[J]. 运筹学学报, 2025 , 29(2) : 201 -213 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.016
The purpose of this paper is to study an approximation theorem and generic convergence of the generalized weakly-mixed vector quasi-equilibrium problem. Firstly, we give an existence theorem for the solution of generalized weakly-mixed vector quasi-equilibrium problems by using the Fan-Knaster-Kuratowski-Mazurkiewicz (Fan-KKM) lemma. Then, based on Simon's bounded rationality theory, we give an approximation theorem for generalized weakly-mixed vector quasi-equilibrium problems in a very general case. Finally, by using Fort's theorem, we obtain a generic convergence result for the solution of generalized weakly-mixed vector quasi-equilibrium problems in the sense of Baire classification.
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