A generalized proximal point algorithm for the nonlinear complementarity problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 33 (1999) no. 4, pp. 447-479.
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     author = {Burachik, Regina S. and Iusem, Alfredo N.},
     title = {A generalized proximal point algorithm for the nonlinear complementarity problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {447--479},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {4},
     year = {1999},
     mrnumber = {1735448},
     zbl = {0961.90117},
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     url = {http://www.numdam.org/item/RO_1999__33_4_447_0/}
}
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Burachik, Regina S.; Iusem, Alfredo N. A generalized proximal point algorithm for the nonlinear complementarity problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 33 (1999) no. 4, pp. 447-479. http://www.numdam.org/item/RO_1999__33_4_447_0/

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. | MR | Zbl

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. | MR | Zbl

3. H. Brezis, Opérateurs Monotones Maximaux et Semi-groupes de Contractions dans les Espaces de Hilbert, North Holland, Amsterdam. | Numdam | Zbl

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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

8. I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar., 1967, 2, p. 299-318. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

12. A. N. Iusem, On some properties of paramonotone operators, J. Convex Analysis, 1998, 5, p. 269-278. | MR | Zbl

13. S. Karamardian, Complementarity problems over cones with monotone and pseudomonotone maps, J. Optim. Theory Appl., 1976, 18, p. 445-455. | MR | Zbl

14. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980. | MR | Zbl

15. M. A. Krasnoselskii, Two observations about the method of successive approximations, Uspekhi Mat. Nauk, 1955, 10, p. 123-127. | MR

16. B. Lemaire, The proximal algorithm, in International Series of Numerical Mathematics, J. P. Penot, Ed., Birkhauser, Basel, 1989, 87, p. 73-87. | Zbl

17. B. Martinet, Régularisation d'inéquations variationelles par approximations succesives, Revue Française d'Informatique et Recherche Opérationnelle, 1970, 2, p. 154-159. | Numdam | MR | Zbl

18. B. Martinet, Algorithmes pour la résolution de problèmes d'optimisation et minimax, Thèse d'État, Université de Grenoble, Grenoble, 1972.

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. | MR | Zbl

20. D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, Editura Academiei, Bucarest, 1978. | MR | Zbl

21. R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 1970, 149, p. 75-88. | MR | Zbl

22. R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 1976, 14, p. 877-898. | MR | Zbl

23. R. T. Rockafellar, Convex Analysis, Princeton University Press, New Jersey, 1970. | MR | Zbl

24. M. Teboulle, Entropic proximal mappings with applications to nonlinear programming. Math. Oper. Res., 1992, 17, p. 97-116. | MR | Zbl

25. M. Teboulle, Convergence of proximal-like algorithms, SIAM J. Optim., 1997, 7, p. 1069-1083. | MR | Zbl