A Distributed Regularized Jacobi-Type ADMM-Method for Generalized Nash Equilibrium Problems in Hilbert Spaces
Eike Börgens, Christian Kanzow · Numerical Functional Analysis and Optimization · 2018
We consider the generalized Nash equilibrium problem in a Hilbert space setting. The joint constraints are eliminated by an augmented Lagrangian-type approach, and we present a fully distributed version by using ideas from alternating direction methods of multipliers (ADMM methods). Convergence follows, under a cocoercivity condition, from the fact that this method can be interpreted as a suitable splitting approach in our Hilbert space endowed with a modified scalar product. This observation also leads to a second algorithmic approach, which yields convergence under a Lipschitz assumption and monotonicity. Numerical results are presented for some examples arising in both finite- and infinite-dimensional Hilbert spaces.