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Many structured convex minimization problems can be modeled by the search of a zero of the sum of two monotone operators. Operator splitting methods have been designed to decompose and regularize at the same time these kind of models. We review here these models and the classical splitting methods. We focus on the numerical sensitivity of these algorithms with respect to the scaling parameters that drive the regularizing terms, in order to accelerate convergence rates for different classes of models.
Lenoir, Arnaud 1 ; Mahey, Philippe 2
@article{RO_2017__51_1_17_0,
author = {Lenoir, Arnaud and Mahey, Philippe},
title = {A survey on operator splitting and decomposition of convex programs},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {17--41},
publisher = {EDP-Sciences},
volume = {51},
number = {1},
year = {2017},
doi = {10.1051/ro/2015065},
zbl = {1360.65169},
mrnumber = {3589262},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2015065/}
}
TY - JOUR AU - Lenoir, Arnaud AU - Mahey, Philippe TI - A survey on operator splitting and decomposition of convex programs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2017 SP - 17 EP - 41 VL - 51 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro/2015065/ DO - 10.1051/ro/2015065 LA - en ID - RO_2017__51_1_17_0 ER -
%0 Journal Article %A Lenoir, Arnaud %A Mahey, Philippe %T A survey on operator splitting and decomposition of convex programs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2017 %P 17-41 %V 51 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro/2015065/ %R 10.1051/ro/2015065 %G en %F RO_2017__51_1_17_0
Lenoir, Arnaud; Mahey, Philippe. A survey on operator splitting and decomposition of convex programs. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 17-41. doi: 10.1051/ro/2015065
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