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Optimization Letters

, Volume 3, Issue 3, pp 419–435 | Cite as

On solving generalized Nash equilibrium problems via optimization

  • Barbara Panicucci
  • Massimo Pappalardo
  • Mauro Passacantando
Original Paper

Abstract

This paper deals with the generalized Nash equilibrium problem (GNEP), i.e. a noncooperative game in which the strategy set of each player, as well as his payoff function, depends on the strategies of all players. We consider an equivalent optimization reformulation of GNEP using a regularized Nikaido–Isoda function so that solutions of GNEP coincide with global minima of the optimization problem. We then propose a derivative-free descent type method with inexact line search to solve the equivalent optimization problem and we prove that our algorithm is globally convergent. The convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of GNEP. Finally, we present the performance of our algorithm on some examples.

Keywords

Generalized Nash equilibrium problem Nikaido–Isoda function Descent method 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Barbara Panicucci
    • 1
  • Massimo Pappalardo
    • 1
  • Mauro Passacantando
    • 1
  1. 1.Department of Applied MathematicsUniversity of PisaPisaItaly

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