The perturbed generalized proximal point algorithm

P. Alexandre; V. H. Nguyen; P. Tossings

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 2, page 223-253
  • ISSN: 0764-583X

How to cite

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Alexandre, P., Nguyen, V. H., and Tossings, P.. "The perturbed generalized proximal point algorithm." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.2 (1998): 223-253. <http://eudml.org/doc/193873>.

@article{Alexandre1998,
author = {Alexandre, P., Nguyen, V. H., Tossings, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {proximal point algorithm; maximal monotone operator; Hilbert space; variable metric; variational convergence theory},
language = {eng},
number = {2},
pages = {223-253},
publisher = {Dunod},
title = {The perturbed generalized proximal point algorithm},
url = {http://eudml.org/doc/193873},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Alexandre, P.
AU - Nguyen, V. H.
AU - Tossings, P.
TI - The perturbed generalized proximal point algorithm
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 2
SP - 223
EP - 253
LA - eng
KW - proximal point algorithm; maximal monotone operator; Hilbert space; variable metric; variational convergence theory
UR - http://eudml.org/doc/193873
ER -

References

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  1. [1] P. ALEXANDRE, 1995, Algorithmes à métrique variable pour la recherche de zéros d'opérateurs maximaux monotones, Thèse d'État, Université de Liège. 
  2. [2] P. ALEXANDRE, P. TOSSINGS, 1996, The Generalized Variational Metric, Working paper, G.E.M.M.E., N° 9604, Université de Liège. 
  3. [3] J. F. BONNANS, J. C. GILBERT, C. LEMARÉCHAL, C. SAGASTIZABAL, février 1993, A family of variable metric proximal methods, Rapport de recherche INRIA 1851. Zbl0832.90102
  4. [4] G. CHEN, M. TEBOULLE, 1993, Convergence analysis of a proximal-like minimization algorithm using Bregman functions, SIAM Journal on Optimization, vol. 3, 3, pp. 538-543. Zbl0808.90103MR1230155
  5. [5] G. COHEN, 1980, Auxiliary problem principle and decomposition of optimization problems, JOTA, vol. 32, 3, pp. 277-305. Zbl0417.49046MR607601
  6. [6] G. COHEN, 1988, Auxiliary problem principle extended to variational inequalities, JOTA, vol. 59, 2, pp. 325-334. Zbl0628.90066MR974037
  7. [7] J. ECKSTEIN, 1993, Nonlinear proximal point algorithm using Bregman functions, MOR, vol. 18, 1, pp. 202-226. Zbl0807.47036MR1250114
  8. [8] S. KABBADJ, 1994, Méthodes proximales entropiques, Thèse Université Montpellier II. 
  9. [9] B. LEMAIRE, 1988, Coupling Optimization Methods and Variational Convergence, Trends in Mathematical Optimization International Series of Num. Math., K. H. Hoffmann, J. B. Hiriart Urruty. C. Lemarechal, J. Zowe, editors, Birkhäuser Verlag, Basel, vol. 84, pp 163-179. Zbl0633.49010MR1017952
  10. [10] B. MARTINET, 1972, Algorithmes pour la résolution de problèmes d'optimisation et de minimax, Thèse d'État, Université de Grenoble. 
  11. [11] M. QIAN, 1992, The Variable Metric Proximal Point Algorithm: Global and Super-linear Convergence, Manuscript, Department of Mathematics, GN-50, University of Washington, Seattle, WA 98195. 
  12. [12] M. QIAN, 1992, The Variable Metric Proximal Point Algorithm: Application to Optimization, Manuscript, Department of Mathematics, GN-50, University of Washington, Seattle, WA 98195. 
  13. [13] A. RENAUD, 1993, Algorithmes de régularisation et décomposition pour les problèmes variationnels monotones, Thèse de doctorat, E.N.S. des Mines de Paris. 
  14. [14] R. T. ROCKAFELLAR, 1976, Monotone Operators and the Proximal Point Algorithm, SIAM J. Control and Optimization, vol. 14, 5, pp 877-898. Zbl0358.90053MR410483
  15. [15] P. TOSSINGS, 1990, Sur les zéros des opérateurs maximaux monotones et applications, Thèse d'État, Université de Liège. 

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