An approximation theorem and generic convergence for equilibrium problems

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by th...

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Published in:	Journal of inequalities and applications Vol. 2018; no. 1; pp. 30 - 12
Main Authors:	Qiu, Xiaoling, Jia, Wensheng, Peng, Dingtao
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 2018 SpringerOpen
Subjects:	Analysis Applications of Mathematics Approximation theorem Equilibrium problems Generic convergence Mathematics Mathematics and Statistics Pseudocontinuity Set-valued mapping Pseudocontinuity Generic convergence Approximation theorem Equilibrium problems Set-valued mapping
ISSN:	1029-242X, 1025-5834, 1029-242X
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Abstract	In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases.
AbstractList	Abstract In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases. In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon's bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases. In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon's bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases.In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon's bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases.
ArticleNumber	30
Author	Jia, Wensheng Qiu, Xiaoling Peng, Dingtao
Author_xml	– sequence: 1 givenname: Xiaoling surname: Qiu fullname: Qiu, Xiaoling organization: School of Mathematics and Statistic, Guizhou University – sequence: 2 givenname: Wensheng surname: Jia fullname: Jia, Wensheng email: jws0505@163.com organization: School of Mathematics and Statistic, Guizhou University, College of Science and Technology, Guizhou University – sequence: 3 givenname: Dingtao surname: Peng fullname: Peng, Dingtao organization: School of Mathematics and Statistic, Guizhou University
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Snippet	In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is... In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon's bounded rationality is... Abstract In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded...
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SubjectTerms	Analysis Applications of Mathematics Approximation theorem Equilibrium problems Generic convergence Mathematics Mathematics and Statistics Pseudocontinuity Set-valued mapping
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Title	An approximation theorem and generic convergence for equilibrium problems
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