Learning how to Play Nash, Potential Games and Alternating Minimization Method for Structured Nonconvex Problems on Riemannian Manifolds - Aix-Marseille Université Accéder directement au contenu
Article Dans Une Revue Journal of Convex Analysis Année : 2013

Learning how to Play Nash, Potential Games and Alternating Minimization Method for Structured Nonconvex Problems on Riemannian Manifolds

Résumé

We consider minimization problems with constraints. We show that if the set of constraints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfies the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We prove that the sequence generated by our algorithm is well defined and converges to an inertial Nash equilibrium under mild assumptions about the objective function. As an application, we give a welcome result on the difficult problem of "learning how to play Nash" (convergence, convergence in finite time, speed of convergence, constraints in action spaces in the context of "alternating potential games" with inertia).
Fichier non déposé

Dates et versions

hal-01500875 , version 1 (03-04-2017)

Identifiants

  • HAL Id : hal-01500875 , version 1

Citer

Joao Xavier Cruz Neto, Paulo Roberto Oliveira, A. Soares Jr Pedro, Antoine Soubeyran. Learning how to Play Nash, Potential Games and Alternating Minimization Method for Structured Nonconvex Problems on Riemannian Manifolds. Journal of Convex Analysis, 2013, 20 (2), pp.395-438. ⟨hal-01500875⟩
132 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More