In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generated by the algorithm is convergent for the pseudomonotone case and assuming an extra condition on the solution set we prove the convergence for the quasimonotone case. This approach unifies the results obtained by Auslender et al. [Math Oper. Res. 24 (1999) 644–688] and Brito et al. [J. Optim. Theory Appl. 154 (2012) 217–234] and extends the convergence properties for the class of φ-divergence distances and Bregman distances.
Accepté le :
DOI : 10.1051/ro/2017078
Mots-clés : Variational inequalities, proximal distance, proximal point algorithm, quasimonotone and pseudomonotone mapping
@article{RO_2018__52_1_159_0,
author = {Papa Quiroz, E.A. and Mallma Ramirez, L. and Oliveira, P.R.},
title = {An inexact algorithm with proximal distances for variational inequalities},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {159--176},
publisher = {EDP-Sciences},
volume = {52},
number = {1},
year = {2018},
doi = {10.1051/ro/2017078},
mrnumber = {3812474},
zbl = {1397.65099},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2017078/}
}
TY - JOUR AU - Papa Quiroz, E.A. AU - Mallma Ramirez, L. AU - Oliveira, P.R. TI - An inexact algorithm with proximal distances for variational inequalities JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 159 EP - 176 VL - 52 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2017078/ DO - 10.1051/ro/2017078 LA - en ID - RO_2018__52_1_159_0 ER -
%0 Journal Article %A Papa Quiroz, E.A. %A Mallma Ramirez, L. %A Oliveira, P.R. %T An inexact algorithm with proximal distances for variational inequalities %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 159-176 %V 52 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2017078/ %R 10.1051/ro/2017078 %G en %F RO_2018__52_1_159_0
Papa Quiroz, E.A.; Mallma Ramirez, L.; Oliveira, P.R. An inexact algorithm with proximal distances for variational inequalities. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 1, pp. 159-176. doi : 10.1051/ro/2017078. http://archive.numdam.org/articles/10.1051/ro/2017078/
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