A generalized proximal point algorithm for the nonlinear complementarity problem

Regina S. Burachik; Alfredo N. Iusem

RAIRO - Operations Research - Recherche Opérationnelle (1999)

  • Volume: 33, Issue: 4, page 447-479
  • ISSN: 0399-0559

How to cite

top

Burachik, Regina S., and Iusem, Alfredo N.. "A generalized proximal point algorithm for the nonlinear complementarity problem." RAIRO - Operations Research - Recherche Opérationnelle 33.4 (1999): 447-479. <http://eudml.org/doc/105200>.

@article{Burachik1999,
author = {Burachik, Regina S., Iusem, Alfredo N.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {nonlinear complementarity problem; proximal point methods; monotone operators},
language = {eng},
number = {4},
pages = {447-479},
publisher = {EDP-Sciences},
title = {A generalized proximal point algorithm for the nonlinear complementarity problem},
url = {http://eudml.org/doc/105200},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Burachik, Regina S.
AU - Iusem, Alfredo N.
TI - A generalized proximal point algorithm for the nonlinear complementarity problem
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1999
PB - EDP-Sciences
VL - 33
IS - 4
SP - 447
EP - 479
LA - eng
KW - nonlinear complementarity problem; proximal point methods; monotone operators
UR - http://eudml.org/doc/105200
ER -

References

top
  1. 1. A. AUSLENDER and M. HADDOU, An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities, Math. Programming, 1995, 71, p. 77-100. Zbl0855.90095MR1362959
  2. 2. L. M. BREGMAN, The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming, U.S.S.R. Comput. Math. and Math. Phys., 1967, 7, n° 3, p. 200-217. Zbl0186.23807MR215617
  3. 3. H. BREZIS, Opérateurs Monotones Maximaux et Semi-groupes de Contractions dans les Espaces de Hilbert, North Holland, Amsterdam. Zbl0169.18701
  4. 4. H. BREZIS and A. HARAUX, Image d'une somme d'opérateurs monotones et applications, Israel J. Math., 1976, 23, n° 2, p. 165-186. Zbl0323.47041MR399965
  5. 5. F. E. BROWDER, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, 1976, 18, n° 2. Zbl0327.47022MR405188
  6. 6. R. S. BURACHIK and A. N. IUSEM, A generalized proximal point algorithm for the variational inequality problem in a Hilbert space, SIAM J. Optim., 1998, 8, p. 197-216. Zbl0911.90273MR1617443
  7. 7. Y. CENSOR, A. N. IUSEM and S. A. ZENIOS, An interior point method with Bregman functions for the variational inequality problem with paramonotone operators, Math. Programming, 1998, 81, p. 373-400. Zbl0919.90123MR1617732
  8. 8. I. CSISZÁR, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar., 1967, 2, p. 299-318. Zbl0157.25802MR219345
  9. 9. P. T. HARKER and J. S. PANG, Finite dimensional variational inequalities and nonlinear complementarity problems: A survey of theory, algorithms and applications, Math. Programming, 1990, 48, p. 161-220. Zbl0734.90098MR1073707
  10. 10. A. N. IUSEM, B. F. SVAITER and M. TEBOULLE, Entropy-like proximal methods in convex programming, Math. Oper. Res., 1994, 19, p. 790-814. Zbl0821.90092MR1304625
  11. 11. A. N. IUSEM and M. TEBOULLE, Convergence rate analysis of nonquadratic proximal and augmented Lagrangian methods for convex and linear programming, Math. Oper. Res., 1995, 20, p. 657-677. Zbl0845.90099MR1354775
  12. 12. A. N. IUSEM, On some properties of paramonotone operators, J. Convex Analysis, 1998, 5, p. 269-278. Zbl0914.90216MR1670352
  13. 13. S. KARAMARDIAN, Complementarity problems over cones with monotone and pseudomonotone maps, J. Optim. Theory Appl., 1976, 18, p. 445-455. Zbl0304.49026MR472053
  14. 14. D. KINDERLEHRER and G. STAMPACCHIA, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980. Zbl0457.35001MR567696
  15. 15. M. A. KRASNOSELSKII, Two observations about the method of successive approximations, Uspekhi Mat. Nauk, 1955, 10, p. 123-127. MR68119
  16. 16. B. LEMAIRE, The proximal algorithm, in International Series of Numerical Mathematics, J. P. Penot, Ed., Birkhauser, Basel, 1989, 87, p. 73-87. Zbl0692.90079
  17. 17. B. MARTINET, Régularisation d'inéquations variationelles par approximations succesives, Revue Française d'Informatique et Recherche Opérationnelle, 1970, 2, p. 154-159. Zbl0215.21103MR298899
  18. 18. B. MARTINET, Algorithmes pour la résolution de problèmes d'optimisation et minimax, Thèse d'État, Université de Grenoble, Grenoble, 1972. 
  19. 19. Z. OPIAL, Weak convergence of the sequence of succesive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. (N.S.), 1967, 75, p. 591-597. Zbl0179.19902MR211301
  20. 20. D. PASCALI and S. SBURLAN, Nonlinear Mappings of Monotone Type, Editura Academiei, Bucarest, 1978. Zbl0423.47021MR531036
  21. 21. R. T. ROCKAFELLAR, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 1970, 149, p. 75-88. Zbl0222.47017MR282272
  22. 22. R. T. ROCKAFELLAR, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 1976, 14, p. 877-898. Zbl0358.90053MR410483
  23. 23. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, New Jersey, 1970. Zbl0932.90001MR274683
  24. 24. M. TEBOULLE, Entropic proximal mappings with applications to nonlinear programming. Math. Oper. Res., 1992, 17, p. 97-116. Zbl0766.90071MR1177730
  25. 25. M. TEBOULLE, Convergence of proximal-like algorithms, SIAM J. Optim., 1997, 7, p. 1069-1083. Zbl0890.90151MR1479615

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.