A family of extragradient methods for solving equilibrium problems

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Abstract

In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.

Original languageEnglish
Pages (from-to)619-630
Number of pages12
JournalJournal of Industrial and Management Optimization
Volume11
Issue number2
DOIs
Publication statusPublished - 2015

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Extragradient Method
Equilibrium Problem
Numerical methods
Two-step Method
Convergence of Algorithms
Pseudomonotone
Variational Inequality Problem
Lipschitz
Numerical Methods
Numerical Results
Family
Class
Equilibrium problem

Keywords

  • Equilibrium problems
  • Extragradient method
  • Two-step extragradient method
  • Variational inequalities

Cite this

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title = "A family of extragradient methods for solving equilibrium problems",
abstract = "In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.",
keywords = "Equilibrium problems, Extragradient method, Two-step extragradient method, Variational inequalities",
author = "Nguyen, {Thi Phuong Dong} and Jean-Jacques Strodiot and {Van Nguyen}, {Thi Thu} and Nguyen, {Van Hien}",
year = "2015",
doi = "10.3934/jimo.2015.11.619",
language = "English",
volume = "11",
pages = "619--630",
journal = "Journal of Industrial and Management Optimization",
issn = "1547-5816",
publisher = "American Institute of Mathematical Sciences",
number = "2",

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T1 - A family of extragradient methods for solving equilibrium problems

AU - Nguyen, Thi Phuong Dong

AU - Strodiot, Jean-Jacques

AU - Van Nguyen, Thi Thu

AU - Nguyen, Van Hien

PY - 2015

Y1 - 2015

N2 - In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.

AB - In this paper we introduce a class of numerical methods for solving an equilibrium problem. This class depends on a parameter and contains the classical extragradient method and a generalization of the two-step extragradient method proposed recently by Zykina and Melen'chuk for solving variational inequality problems. Convergence of each algorithm of this class to a solution of the equilibrium problem is obtained under the condition that the equilibrium function associated with the problem is pseudomonotone and Lipschitz continuous. Some preliminary numerical results are given to compare the numerical behavior of the two-step extragradient method with respect to the other methods of the class and in particular to the extragradient method.

KW - Equilibrium problems

KW - Extragradient method

KW - Two-step extragradient method

KW - Variational inequalities

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EP - 630

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

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