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 method, equilibrium problem, inexact solution, proximal point method, variational inequality problem
@article{RO_2010__44_1_5_0,
author = {Iusem, Alfredo N. and Nasri, Mostafa},
title = {Augmented lagrangian methods for variational inequality problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {5--25},
year = {2010},
publisher = {EDP Sciences},
volume = {44},
number = {1},
doi = {10.1051/ro/2010006},
mrnumber = {2642913},
zbl = {1187.90293},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2010006/}
}
TY - JOUR AU - Iusem, Alfredo N. AU - Nasri, Mostafa TI - Augmented lagrangian methods for variational inequality problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2010 SP - 5 EP - 25 VL - 44 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2010006/ DO - 10.1051/ro/2010006 LA - en ID - RO_2010__44_1_5_0 ER -
%0 Journal Article %A Iusem, Alfredo N. %A Nasri, Mostafa %T Augmented lagrangian methods for variational inequality problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2010 %P 5-25 %V 44 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2010006/ %R 10.1051/ro/2010006 %G en %F RO_2010__44_1_5_0
Iusem, Alfredo N.; Nasri, Mostafa. Augmented lagrangian methods for variational inequality problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 1, pp. 5-25. doi: 10.1051/ro/2010006
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