Journal of Global Optimization

, Volume 53, Issue 4, pp 587–614 | Cite as

Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems

Article

Abstract

Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of the player convex generalized Nash equilibrium problem (GNEP). Further we give an unconstrained reformulation of a large subclass of player convex GNEPs which, in particular, includes the jointly convex GNEPs. Both approaches characterize all solutions of a GNEP as minima of optimization problems. The smoothness properties of these optimization problems are discussed in detail, and it is shown that the corresponding objective functions are continuous and piecewise continuously differentiable under mild assumptions. Some numerical results based on the unconstrained optimization reformulation being applied to player convex GNEPs are also included.

Keywords

Generalized Nash equilibrium problem Jointly convex Player convex Optimization reformulation Continuity PC1mapping Constant rank constraint qualification 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany
  2. 2.Karlsruhe Institute of TechnologyInstitute of Operations ResearchKarlsruheGermany

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