Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 730-737.

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An Approximation Theorem of Variational Inequalities Under Bounded Rationality

Xiaoling Qiu,Wensheng Jia*()   

  1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025
  • Received:2018-04-26 Online:2019-08-26 Published:2019-09-11
  • Contact: Wensheng Jia
  • 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)


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