Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Minimax Theory and its Applications 09 (2024), No. 1, 055--084
Copyright Heldermann Verlag 2024

Linear and Superlinear Convergence of a Potential Reduction Algorithm for Generalized Nash Equilibrium Problems

Axel Dreves
Dept. of Aerospace Engineering, nst. for Applied Mathematics and Scientific Computing, Universität der Bundeswehr, München - Neubiberg, Germany

We present a detailed convergence analysis of the potential reduction algorithm for generalized Nash equilibrium problems (GNEPs), that is known to be a robust method for solving those problems. We prove Q-linear convergence of the merit function and R-linear convergence of the distance of the iterates to the set of KKT-points of the GNEP. Furthermore, we show that the stepsize is bounded from below, implying finite termination of the method for prescribed accuracy. Using a non-fixed linesearch parameter we prove superlinear convergence. Further, we give additional assumptions to transfer the convergence rates to an inexact potential reduction algorithm. By our analysis, we also discover indicators that could be used to estimate the active set at an accumulation point, and hence at a generalized Nash equilibrium, which might be exploited numerically.

Keywords: Generalized Nash equilibrium problem, potential reduction algorithm, linear convergence, superlinear convergence.

MSC: 90C30, 90C51, 91A10, 65B99.

[ Fulltext-pdf  (220  KB)] for subscribers only.