Strict convex regularizations, proximal points and augmented lagrangians
RAIRO - Operations Research - Recherche Opérationnelle, Volume 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},
     mrnumber = {1786463},
     zbl = {1029.90069},
     language = {en},
     url = {http://archive.numdam.org/item/RO_2000__34_3_283_0/}
}
TY  - JOUR
AU  - Humes Jr., Carlos
AU  - Da silva E Silva, Paulo José
TI  - Strict convex regularizations, proximal points and augmented lagrangians
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2000
SP  - 283
EP  - 303
VL  - 34
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/item/RO_2000__34_3_283_0/
LA  - en
ID  - RO_2000__34_3_283_0
ER  - 
%0 Journal Article
%A Humes Jr., Carlos
%A Da silva E Silva, Paulo José
%T Strict convex regularizations, proximal points and augmented lagrangians
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2000
%P 283-303
%V 34
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/item/RO_2000__34_3_283_0/
%G en
%F RO_2000__34_3_283_0
Humes Jr., Carlos; Da silva E Silva, Paulo José. Strict convex regularizations, proximal points and augmented lagrangians. RAIRO - Operations Research - Recherche Opérationnelle, Volume 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 | Zbl

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

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

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

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

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

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

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 | Zbl

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

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

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

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

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

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

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

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

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

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 | Zbl

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

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 | Zbl

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

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