Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium Problems

TL;DR

This paper introduces an augmented Lagrangian algorithm for solving generalized Nash equilibrium problems, analyzing its convergence, optimality, and practical performance through numerical experiments.

Contribution

It develops a novel augmented Lagrangian method tailored for GNEPs, including convergence analysis and a modification for variational equilibria computation.

Findings

The method converges under certain constraint qualifications.

The algorithm effectively computes variational equilibria.

Numerical results demonstrate practical efficiency.

Abstract

We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard to both feasibility and optimality of limit points. This is done by introducing a secondary GNEP as a new optimality concept. In this context, special consideration is given to the role of suitable constraint qualifications that take into account the particular structure of GNEPs. Furthermore, we consider the behaviour of the method for jointly-convex GNEPs and describe a modification which is tailored towards the computation of variational equilibria. Numerical results are included to illustrate the practical performance of the overall method.