A New Error Bound Result for Generalized Nash Equilibrium Problems and its Algorithmic Application

Axel Dreves(axel.drevesunibw.de)
Francisco Facchinei(facchineidis.uniroma1.it)
Andreas Fischer(Andreas.Fischertu-dresden.de)
Markus Herrich(Markus.Herrichtu-dresden.de)

Abstract: We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that is weaker than known ones. In particular, this condition implies neither local uniqueness of a solution nor strict complementarity. We also report promising numerical results.

Keywords: Generalized Nash Equilibrium Problem, Potential reduction algorithm, LP-Newton method, global convergence, local quadratic convergence, local error bound condition

Category 1: Complementarity and Variational Inequalities

Category 2: Other Topics (Game Theory )

Category 3: Nonlinear Optimization (Other )

Citation: Report MATH-NM-1-2013, Institute of Numerical Mathematics, TU Dresden, 01062 Dresden, Germany, January 2013

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Entry Submitted: 02/11/2013
Entry Accepted: 02/11/2013
Entry Last Modified: 02/11/2013

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