Journal of Global Optimization

, Volume 56, Issue 2, pp 373–397 | Cite as

A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems

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


Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.


Quasi-equilibrium problems Quasi-variational inequalities Hybrid extragradient methods Generalized Nash equilibrium problems 

Mathematics Subject Classification (2000)

49J40 65K10 91A12 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Jean Jacques Strodiot
    • 1
    • 2
  • Thi Thu Van Nguyen
    • 1
  • Van Hien Nguyen
    • 1
    • 2
  1. 1.Institute for Computational Science and TechnologyHo Chi Minh CityVietnam
  2. 2.Department of MathematicsUniversity of NamurNamurBelgium

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