Augmented lagrangian methods for variational inequality problems
RAIRO - Operations Research - Recherche Opérationnelle, Volume 44 (2010) no. 1, pp. 5-25.

We introduce augmented lagrangian methods for solving finite dimensional variational inequality 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 variational inequality problem, and then dual variables are updated through a closed formula. A full convergence analysis is provided, allowing for inexact solution of the subproblems.

DOI: 10.1051/ro/2010006
Classification: 90C47, 49J35
Keywords: augmented lagrangian method, equilibrium problem, inexact solution, proximal point method, variational inequality problem
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Iusem, Alfredo N.; Nasri, Mostafa. Augmented lagrangian methods for variational inequality problems. RAIRO - Operations Research - Recherche Opérationnelle, Volume 44 (2010) no. 1, pp. 5-25. doi : 10.1051/ro/2010006. http://archive.numdam.org/articles/10.1051/ro/2010006/

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