有限理性下变分不等式的逼近定理

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 730-737.

有限理性下变分不等式的逼近定理

丘小玲,贾文生*()

贵州大学数学与统计学院贵阳 550025

收稿日期:2018-04-26 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 贾文生 E-mail:jws0505@163.com
基金资助:
国家自然科学基金(11561013);人社部留学归国人员择优资助项目(2015192);贵州省科技厅联合基金(QKH[2014]7643);贵州省科技厅联合基金([2016]7425);贵州大学引进人才基金(201405);贵州大学引进人才基金(201811)

An Approximation Theorem of Variational Inequalities Under Bounded Rationality

Xiaoling Qiu,Wensheng Jia*()

School of Mathematics and Statistics, Guizhou University, Guiyang 550025

Received:2018-04-26 Online:2019-08-26 Published:2019-09-11
Contact: Wensheng Jia E-mail:jws0505@163.com
Supported by:
the NSFC(11561013);the Project for the Selection of Returnees from Overseas Studies by the Ministry of Human Resources and Social Sciences(2015192);the Science and Technology Foundation of Guizhou Province(QKH[2014]7643);the Science and Technology Foundation of Guizhou Province([2016]7425);the Introduced Talent Foundation of Guizhou University(201405);the Introduced Talent Foundation of Guizhou University(201811)

摘要/Abstract

摘要：

该文基于Simon的有限理性理论，首先构造了有限理性下变分不等式问题的逼近定理，为有关变分不等式问题的不同算法提供了一个理论支持，充分体现了有限理性是对完全理性的逼近，是以完全理性为终极目标的.然后，利用集值分析的方法，将有限理性的逼近定理应用于变分不等式问题解的收敛性分析，在Baire分类的意义下，分别得到了函数扰动及函数和约束集同时扰动两种情况下单调变分不等式问题的解具有通有收敛性的结果.

关键词: 有限理性, 单调变分不等式, 逼近定理, 集值映射, 通有收敛

Abstract:

In this paper, basing on Simon's bounded rationality theory, we first prove and construct an approximation theorem for variational inequalities problems, which provide theoretical support for many relevant different algorithms. Simon's bounded rationality is illustrated and bounded rationality is approaching to full rationality as its ultimate goal. Then, by the methods of set-valued analysis, bounded rationality approximation theory is used for the convergence analysis of solutions of variational inequalities problems. In the sense of Baire category, we obtain the generic convergence of the solutions of monotone variational inequalities problems, in both cases that the function disturbance and the function and constraint set disturbance.

Key words: Bounded rationality, Monotone variational inequalities, Approximation theorem, Set-valued mapping, Generic convergence

中图分类号:

O221

丘小玲,贾文生. 有限理性下变分不等式的逼近定理[J]. 数学物理学报, 2019, 39(4): 730-737.

Xiaoling Qiu,Wensheng Jia. An Approximation Theorem of Variational Inequalities Under Bounded Rationality[J]. Acta mathematica scientia,Series A, 2019, 39(4): 730-737.

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