Augmented Lagrangian methods for variational inequality problems

Augmented Lagrangian methods for variational inequality problems

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Article ID: iaor20101889
Volume: 44
Issue: 1
Start Page Number: 5
End Page Number: 25
Publication Date: Jan 2010
Journal: RAIRO Operations Research
Authors: ,
Keywords: optimization
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.

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