# Augmented Lagrangian methods for variational inequality problems

Alfredo N. Iusem; Mostafa Nasri

RAIRO - Operations Research (2010)

- Volume: 44, Issue: 1, page 5-25
- ISSN: 0399-0559

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topIusem, Alfredo N., and Nasri, Mostafa. "Augmented Lagrangian methods for variational inequality problems." RAIRO - Operations Research 44.1 (2010): 5-25. <http://eudml.org/doc/250859>.

@article{Iusem2010,

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.
},

author = {Iusem, Alfredo N., Nasri, Mostafa},

journal = {RAIRO - Operations Research},

keywords = {Augmented Lagrangian method; equilibrium problem; inexact solution; proximal point method; variational
inequality problem},

language = {eng},

month = {2},

number = {1},

pages = {5-25},

publisher = {EDP Sciences},

title = {Augmented Lagrangian methods for variational inequality problems},

url = {http://eudml.org/doc/250859},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Iusem, Alfredo N.

AU - Nasri, Mostafa

TI - Augmented Lagrangian methods for variational inequality problems

JO - RAIRO - Operations Research

DA - 2010/2//

PB - EDP Sciences

VL - 44

IS - 1

SP - 5

EP - 25

AB -
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.

LA - eng

KW - Augmented Lagrangian method; equilibrium problem; inexact solution; proximal point method; variational
inequality problem

UR - http://eudml.org/doc/250859

ER -

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