A Distributed Regularized Jacobi-Type ADMM-Method for Generalized Nash Equilibrium Problems in Hilbert Spaces. (10th September 2018)

• Record Type: Journal Article
• Authors: Börgens, Eike; Kanzow, Christian
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 12(2018)
• Page Start: 1316
• Page End: 1349
• Publication Date: 2018-09-10
• Subjects: ADMM method -- convergence -- distributed method -- generalized Nash equilibrium problem -- Hilbert space; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1477800
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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.