Preprint A576/2007
Augmented Lagrangian methods for equilibrium problems

Mostafa Nasri | Iusem, Alfredo N.

**Keywords: **
Augmented Lagrangian | equilibrium problem

We introduce Augmented Lagrangian methods for solving finite dimensional equilibrium problems whose feasible sets are defined by convex inequalities, generalizing the proximal Augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained equilibrium problem, and then dual variables are updated through a closed formula. A full convergence analysis is provided, allowing for inexact solution of the subproblems.