Augmented Lagrangian methods for variational inequality problems
Instituto de Matemática Pura e Aplicada,
Estrada Dona Castorina 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil; firstname.lastname@example.org; email@example.com
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.
Mathematics Subject Classification: 90C47 / 49J35
Key words: Augmented Lagrangian method / equilibrium problem / inexact solution / proximal point method / variational inequality problem
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