Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems

Article

Abstract

The gap function (or merit function) is a classic tool for reformulating a Stampacchia variational inequality as an optimization problem. In this paper, we adapt this technique for quasivariational inequalities, that is, variational inequalities in which the constraint set depends on the current point. Following Fukushima (J. Ind. Manag. Optim. 3:165–171, 2007), an axiomatic approach is proposed. Error bounds for quasivariational inequalities are provided and an application to generalized Nash equilibrium problems is also considered.

Keywords

Gap function Merit function Set-valued map Quasivariational inequality Nash equilibrium 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Lab. PROMES, UPR 8521Université de PerpignanPerpignanFrance
  2. 2.Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile

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