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Computational Optimization and Applications

, Volume 69, Issue 3, pp 629–652 | Cite as

A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties

  • Leonardo GalliEmail author
  • Christian Kanzow
  • Marco Sciandrone
Article
  • 204 Downloads

Abstract

The generalized Nash equilibrium problem (GNEP) is often difficult to solve by Newton-type methods since the problem tends to have locally nonunique solutions. Here we take an existing trust-region method which is known to be locally fast convergent under a relatively mild error bound condition, and modify this method by a nonmonotone strategy in order to obtain a more reliable and efficient solver. The nonmonotone trust-region method inherits the nice local convergence properties of its monotone counterpart and is also shown to have the same global convergence properties. Numerical results indicate that the nonmonotone trust-region method is significantly better than the monotone version, and is at least competitive to an existing software applied to the same reformulation used within our trust-region framework. Additional tests on quasi-variational inequalities (QVI) are also presented to validate efficiency of the proposed extension.

Keywords

Generalized Nash equilibrium problem Trust-region algorithm Nonmonotone strategy Global convergence Local superlinear convergence Quasi-variational inequalities 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Information EngineeringUniversity of FlorenceFlorenceItaly
  2. 2.Institute of MathematicsUniversity of WürzburgWürzburgGermany

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