Partial regularization of the sum of two maximal monotone operators
Mahey, P. ; Tao, Pham Dinh
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993), p. 375-392 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{M2AN_1993__27_3_375_0,
     author = {Mahey, P. and Tao, Pham Dinh},
     title = {Partial regularization of the sum of two maximal monotone operators},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {27},
     year = {1993},
     pages = {375-392},
     mrnumber = {1221060},
     zbl = {0778.65042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1993__27_3_375_0}
}

Mahey, P.; Tao, Pham Dinh. Partial regularization of the sum of two maximal monotone operators. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 27 (1993) pp. 375-392. http://gdmltest.u-ga.fr/item/M2AN_1993__27_3_375_0/

[1] H. Attouch, Variational convergence for functions and operators, Pitman, 1984. | MR 773850 | Zbl 0561.49012

[2] D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation, Prentice-Hall Int., 1989. | Zbl 0743.65107

[3] M. A. Boughazi, Contribution à l'étude des algorithmes d'optimisation en Analyse des Données, Thèse de Doctorat, Université de Grenoble, 1987.

[4] H. Brezis, Opérateurs maximaux monotones, Mathematics Studies 5, North Holland, 1973.

[5] H. Brezis and P. L. Lions, Produits infinis de résolvantes, Israel J. of Math.29, 4, 1978, pp. 329-345. | MR 491922 | Zbl 0387.47038

[6] F. Browder and W. Petryshin, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. of Math. Anal and Appl. 20, 1967, pp. 197-228. | MR 217658 | Zbl 0153.45701

[7] J. Lemordant and T. Pham Dinh, Algorithme proximal pour la résolution numérique d'équations d'évolution en vison de bas niveau, preprint.

[8] P. L. Lions, Une méthode itérative de résolution d'une inéquation variationnelle, Israel J. of Math. 31, 2, 1978, pp. 204-208. | MR 516257 | Zbl 0395.49013

[9] P. L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal. 16, 6, 1979, pp. 964-979. | MR 551319 | Zbl 0426.65050

[10] P. Mahey, H. Van Nguyen and D. T. Pham, Proximal methods and decomposition of large convex programs, ARTEMIS RR877, 1992.

[11] B. Martinet, Algorithmes pour la résolution de problèmes d'optimisation et de minimax, Thèse d'État, Univ. de Grenoble, 1972.

[12] C. Michelot, Problème de localisation : propriétés géométriques etrésolution par des méthodes d'optimisation, Thèse de Doctorat, Université de Bourgogne, 1988.

[13] J. J. Moreau, Proximité et dualité dans un espace Hilbertien, Bull. Soc. Math. France 93, 1965, pp. 273-299. | Numdam | MR 201952 | Zbl 0136.12101

[14] G. B. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert spaces, J. of Math, Anal and Appl. 72, 1979 pp. 383-390. | MR 559375 | Zbl 0428.47039

[15] G. Pierra G., Decomposition through formalization in a product space, Math. Prog. 28, 1984, pp. 96-115. | MR 727421 | Zbl 0523.49022

[16] R. T. Rockafellar, Convex analysis, Princeton University Press, 1970. | MR 274683 | Zbl 0193.18401

[17] R. T. Rockafellar, Monotone operators and the proximal point algorithm in convex programming, SIAM J. on Control and Optim. 14, 1976, pp. 877-898. | MR 410483 | Zbl 0358.90053

[18] R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149, 1970, pp. 75-88. | MR 282272 | Zbl 0222.47017

[19] J. E. Spingarn, Partial inverse of a monotone operator, Appl. Math. Optim. 10, 1983, pp. 247-265. | MR 722489 | Zbl 0524.90072

[20] G. Stampacchia, Variational inequalities, in Theory and Applications of Monotone Operators, A. Ghizetti, 1969. | MR 425699 | Zbl 0247.47050

[21] A. Yassine, Études adaptatives et comparatives de certains algorithmes en optimisation. Implémentations effectives et applications, Thèse de Doctorat, Université de Grenoble, 1989.