[Une représentation des opérateurs maximaux monotones par des fonctions convexes et son impact sur les règles de calcul]
Nous introduisons une représentation nouvelle pour les opérateurs maximaux monotones à l'aide de fonctions convexes. Nous la relions à des représentations dues à Krauss, Fitzpatrick, Martı́nez-Legaz et Théra. Nous montrons son utilité pour obtenir des règles de composition et de somme.
We introduce a new representation for maximal monotone operators. We relate it to previous representations given by Krauss, Fitzpatrick and Martı́nez-Legaz and Théra. We show its usefulness for the study of compositions and sums of maximal monotone operators.
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@article{CRMATH_2004__338_11_853_0,
author = {Penot, Jean-Paul},
title = {A representation of maximal monotone operators by closed convex functions and its impact on calculus rules},
journal = {Comptes Rendus. Math\'ematique},
pages = {853--858},
publisher = {Elsevier},
volume = {338},
number = {11},
year = {2004},
doi = {10.1016/j.crma.2004.03.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.03.017/}
}
TY - JOUR AU - Penot, Jean-Paul TI - A representation of maximal monotone operators by closed convex functions and its impact on calculus rules JO - Comptes Rendus. Mathématique PY - 2004 SP - 853 EP - 858 VL - 338 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.03.017/ DO - 10.1016/j.crma.2004.03.017 LA - en ID - CRMATH_2004__338_11_853_0 ER -
%0 Journal Article %A Penot, Jean-Paul %T A representation of maximal monotone operators by closed convex functions and its impact on calculus rules %J Comptes Rendus. Mathématique %D 2004 %P 853-858 %V 338 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.03.017/ %R 10.1016/j.crma.2004.03.017 %G en %F CRMATH_2004__338_11_853_0
Penot, Jean-Paul. A representation of maximal monotone operators by closed convex functions and its impact on calculus rules. Comptes Rendus. Mathématique, Tome 338 (2004) no. 11, pp. 853-858. doi : 10.1016/j.crma.2004.03.017. http://www.numdam.org/articles/10.1016/j.crma.2004.03.017/
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