Strict convex regularizations, proximal points and augmented lagrangians
RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 3, pp. 283-303.
@article{RO_2000__34_3_283_0,
     author = {Humes Jr., Carlos and Da silva E Silva, Paulo Jos\'e},
     title = {Strict convex regularizations, proximal points and augmented lagrangians},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {283--303},
     publisher = {EDP-Sciences},
     volume = {34},
     number = {3},
     year = {2000},
     zbl = {1029.90069},
     mrnumber = {1786463},
     language = {en},
     url = {http://archive.numdam.org/item/RO_2000__34_3_283_0/}
}
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Humes Jr., Carlos; Da silva E Silva, Paulo José. Strict convex regularizations, proximal points and augmented lagrangians. RAIRO - Operations Research - Recherche Opérationnelle, Tome 34 (2000) no. 3, pp. 283-303. http://archive.numdam.org/item/RO_2000__34_3_283_0/

1. A. Auslender, R. Cominetti and M. Haddou, Asymptotic analysis for penalty and barrier methods in convex and linear programming. Math. Oper. Res. 22 (1997) 43-62. | MR 1436573 | Zbl 0872.90067

2. D. Bertsekas, Constrained Optimization and Lagrange Multipliers. Academic Press, New York (1982). | MR 690767

3. D. Bertsekas, Nonlinear Programming. Athena Scientific (1995). | Zbl 1015.90077

4. Y. Censor and J. Zenios, The proximal minimization algorithms with D-functions. J. Optim. Theory Appl. 73 (1992) 451-464. | MR 1164803 | Zbl 0794.90058

5. J. Gauvin, A necessary and sufficient condition to have bounded multipliers in nonconvex programming. Math. Programming 12 (1977) 136-138. | MR 489903 | Zbl 0354.90075

6. A.M. Geoffrion, Duality in non-linear programming, a simplified applications-oriented development. SIAM Rev. 13 (1971) 65-101. | MR 280199 | Zbl 0232.90049

7. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. II. Advanced theory and bundle methods. Springer-Verlag, Berlin (1993). | MR 1295240 | Zbl 0795.49002

8. C. Humes and P. Silva, An inexact classical proximal point algorithm viewed as a descent method in the optimization case. Technical Report RT-MAC 99-10. Instituto de Matemática e Estatística - USP (1999).

9. C. Jr. Humes, Some comments on Lagrangian duality, optimality conditions and convexity. Investigación Oper. 2 (1991) 159-169.

10. A. Iusem, Métodos de Ponto Proximal em Otimização. Instituto de Matemática Pura e Aplicada - CNPq (1995). Book from the 20° Colóquio Brasileiro de Matemática.

11. A. Iusem and M. Teboulle, On the convergence rate of entropic proximal minimization algorithms. Comput. Appl. Math. 12 (1993) 153-168. | MR 1268127 | Zbl 0803.90101

12. A. Iusem, M. Teboulle and B. Svaiter, Entropy-like proximal methods in covex programming. Math. Oper. Res. 19 (1994) 790-814. | MR 1304625 | Zbl 0821.90092

13. P.-J. Laurent, Approximation et Optimisation. Collection Enseignement des Sciences. Hermann (1972). | MR 467080 | Zbl 0238.90058

14. B. Martinet, Régularisation d'inéquations variationelles par approximations successives. Rev. Française Inf. Rech. Oper. (1970) 154-159. | Numdam | MR 298899 | Zbl 0215.21103

15. B. Martinet, Détermination approché d'un point fixe d'une application pseudo-contractante, C.R. Acad. Sci. Paris 274A (1972) 163-165. | MR 290213 | Zbl 0226.47032

16. J. Moreau, Proximité et dualité dans un espace hilbertien. Bull. Soc. Math. France 93 (1965) 273-299. | Numdam | MR 201952 | Zbl 0136.12101

17. R.T. Rockafellar, Extension of Fenchel's duality theorem for convex functions. Duke Math. J. 33 (1966) 81-89. | MR 187062 | Zbl 0138.09301

18. R.T. Rockafellar, Convex Analysis. Princeton University Press (1970). | MR 274683 | Zbl 0932.90001

19. R.T. Rockafellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1 (1976) 97-116. | MR 418919 | Zbl 0402.90076

20. R.T. Rockafellar, Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14 (1976) 887-898. | MR 410483 | Zbl 0358.90053

21. R.T. Rockafellar and R.J.-B. Wets, Variational analysis [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, Grundlehren Math. Wiss. 317 (1998). | MR 1491362 | Zbl 0888.49001

22. M. Solodov and B. Svaiter, A hybrid projection-proximal point algorithm. J. Convex Anal. 6 (1999). | MR 1713951 | Zbl 0961.90128

23. M. Solodov and B. Svaiter, An inexact hybrid extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. Set-Valued Analysis (to appear). | MR 1756912 | Zbl 0959.90038

24. M. Teboulle, Entropic proximal methods with aplications to nonlinear programming. Math. Oper. Res. 17 (1992) 670-690. | MR 1177730 | Zbl 0766.90071

25. J. Tind and L.A. Wolsey, An elementary survey of general duality theory in mathematical programming. Math. Programming 20 (1981) 241-261. | MR 632634 | Zbl 0467.90061