This paper presents an inexact proximal method for solving monotone variational inequality problems with a given separable structure. The proposed algorithm is a natural extension of the Proximal Multiplier Algorithm with Proximal Distances (PMAPD) proposed by Sarmiento et al. [Optimization 65 (2016) 501–537], which unified the works of Chen and Teboulle (PCPM method), and Kyono and Fukushima (NPCPMM) developed for solving convex programs with a particular separable structure. The resulting method combines the recent proximal distances theory introduced by Auslender and Teboulle [SIAM J. Optim. 16 (2006) 697–725] with a decomposition method given by Chen and Teboulle for convex problems and extends the results of the Entropic Proximal Decomposition Method proposed by Auslender and Teboulle, which used to Logarithmic Quadratic proximal distances. Under some mild assumptions on the problem we prove a global convergence of the primal–dual sequences produced by the algorithm.
Keywords: Variational inequalities, maximal monotone operators, separable structure, proximal distances
@article{RO_2021__55_S1_S873_0,
author = {Papa Quiroz, Erik A. and Sarmiento, Orlando and Oliveira, Paulo Roberto},
title = {An inexact proximal decomposition method for variational inequalities with separable structure},
journal = {RAIRO. Operations Research},
pages = {S873--S884},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020018},
mrnumber = {4223087},
zbl = {1472.90142},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020018/}
}
TY - JOUR AU - Papa Quiroz, Erik A. AU - Sarmiento, Orlando AU - Oliveira, Paulo Roberto TI - An inexact proximal decomposition method for variational inequalities with separable structure JO - RAIRO. Operations Research PY - 2021 SP - S873 EP - S884 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020018/ DO - 10.1051/ro/2020018 LA - en ID - RO_2021__55_S1_S873_0 ER -
%0 Journal Article %A Papa Quiroz, Erik A. %A Sarmiento, Orlando %A Oliveira, Paulo Roberto %T An inexact proximal decomposition method for variational inequalities with separable structure %J RAIRO. Operations Research %D 2021 %P S873-S884 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020018/ %R 10.1051/ro/2020018 %G en %F RO_2021__55_S1_S873_0
Papa Quiroz, Erik A.; Sarmiento, Orlando; Oliveira, Paulo Roberto. An inexact proximal decomposition method for variational inequalities with separable structure. RAIRO. Operations Research, Tome 55 (2021), pp. S873-S884. doi: 10.1051/ro/2020018
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