A class of hybrid methods for quasi-variational inequalities

Thi Thu Van Nguyen, Thi Phuong Dong Nguyen, Jean Jacques Strodiot, Van Hien Nguyen

Research output: Contribution to journalArticle


In this paper we develop a new and efficient method for solving a quasi-variational inequality problem (QVIP) by using an extragradient-type method. The strategy is to combine the well-known search directions in the correction step from literature with the direction defined by the current iterate and the trial point obtained in the prediction step. This new combined search direction allows us to improve the convergence of the sequence of iterates to the solution of the QVIP but under a slightly stronger assumption, namely the co-coercivity of the problem operator. The new algorithm is devised to solve problems where the projections onto the moving feasible set are not easy to obtain. This combined procedure is applied to three well-known search directions and numerical illustrations are given to show the improvements obtained thanks to this strategy.

Original languageEnglish
Pages (from-to)2211-2226
Number of pages16
JournalOptimization Letters
Issue number8
Publication statusPublished - 1 Jan 2014



  • Co-coercivity
  • Generalized Nash equilibrium problems
  • Hybrid extragradient methods
  • Quasi-variational inequalities
  • Two-step methods

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