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Augmented Lagrangian methods for variational inequality problems

Published online by Cambridge University Press:  08 February 2010

Alfredo N. Iusem  and
Mostafa Nasri
Alfredo N. Iusem
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil; iusp@impa.br; mostafa@impa.br
Mostafa Nasri
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil; iusp@impa.br; mostafa@impa.br
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Abstract

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.

Keywords

Augmented Lagrangian methodequilibrium probleminexact solutionproximal point methodvariational inequality problem
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 1 , January 2010 , pp. 5 - 25
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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