有限理性下变分不等式的逼近定理

Abstract

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

CLC Number:

O221

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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References 21

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An Approximation Theorem of Variational Inequalities Under Bounded Rationality

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