The interior proximal extragradient method for solving equilibrium problems

  • Thi Thu Van Nguyen
  • Jean-Jacques Strodiot
  • Van Hien Nguyen


In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.


Interior proximal method Logarithmic-quadratic proximal method Extragradient method Armijo-backtracking linesearch Equilibrium problems 


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Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Thi Thu Van Nguyen
    • 1
    • 2
  • Jean-Jacques Strodiot
    • 1
  • Van Hien Nguyen
    • 1
  1. 1.Department of MathematicsUniversity of Namur (FUNDP)NamurBelgium
  2. 2.Faculty of Mathematics and InformaticsUniversity of Natural Sciences, Vietnam National UniversityHo Chi Minh CityVietnam

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