A practical general approximation criterion for methods of multipliers based on Bregman distances

Mathematical Programming, Series B

Volumn 96, Issue 1, 2003, Pages 61-86

  Eckstein, Jonathan ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; DISTANCE MEASUREMENT; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; QUADRATIC PROGRAMMING;

BREGMAN DISTANCE KERNELS; CONVEX PROGRAM; QUADRATIC METHODS;

APPROXIMATION THEORY;

EID: 4944237976     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-003-0374-x     Document Type: Article

References (31)

1. Auslender, A., Teboulle, M., Ben-Tiba, S.: Interior proximal and multiplier methods based on second order homogeneous kernels. Math. Operations Res. 24, 645-668 (1999)
2. Ben-Tal, A., Zibulevsky, M.: Penalty/barrier multiplier methods for convex programming problems. SIAM J. Optimization 7, 347-366 (1997)
3. Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982
4. Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont, MA, 1995
5. Bregman, L. M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Phys. 7, 200-217 (1967)
6. Burachik, R.S., Iusem, A.N., Svaiter, B.F.: Enlargement of monotone operators with applications to variational inequalities. Set-Valued Analysis 5, 159-180 (1997)
7. Censor, Y., Lent, A.: An iterative row-action method for interval convex programming. J. Optimization Theory Appl. 34, 321-353 (1981)
8. Censor, Y., Zenios, S.A.: Proximal minimization algorithm with D-functions. J. Optimization Theory Appl. 73, 451-164 (1992)
9. Chen, G., Teboulle, M.: A convergence analysis of proximal-like minimization algorithms using Bregman functions. SLAM J. Optimization 3, 538-543 (1993)
10. Eckstein, J.: Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming. Math. Operations Res. 18, 202-226 (1993)
11. Eckstein, J.: Approximate iterations in Bregman-function-based proximal algorithms. Math. Programming 83, 113-124 (1998)
12. Eckstein, J., Ferris, M.C.: Smooth methods of multipliers for monotone complementarity problems. Math. Programming 86, 65-90 (1999)
13. Fiacco, A.V., McCormick, G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Classics in Applied Mathematics Vol. 4, SLAM, Philadelphia, 1990
14. Hager, W.W.: Analysis and implementation of a dual algorithm for constrained optimization. J. Optimization Theory Appl. 79, 427-462 (1993)
15. Kiwiel, K.C.: On the twice differentiable augmented Lagrangian. J. Optimization Theory Appl. 88, 233-236 (1996)
16. Kiwiel, K.C.: Proximal minimization methods with generalized Bregman functions. SIAM J. Control Optimization 35, 1142-1168 (1997)
17. Pennanen, T.: Dualization of monotone generalized equations. Ph.D. Thesis, Department of Mathematics, University of Washington, Seattle, 1999
18. Pennanen, T.: Dualization of generalized equations of maximal monotone type. SIAM J. Optim. 10, 809-835 (2000)
19. Polyak, B.: Introduction to Optimization, Optimization Software Inc., New York, 1987
20. Rockafellar, R.T.: Convex Analysis, Princeton University Press, Princeton, NJ, 1970
21. Rockafellar, R.T.: Conjugate Duality and Optimization, CBMS-NSF Regional Conference Serias in Applied Mathematics Vol. 16, SIAM, Philadelphia, 1974
22. Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877-898 (1976)
23. Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Operations Res. 1, 97-116 (1976)
24. Ruszczyriski, A.: On convergence of an augmented Lagrangian decomposition method for sparse convex optimization. Math. Operations Res. 20, 634-656 (1995)
25. da Silva e Silva, P. J.: Topicos em Métodos de Ponto Proximal. Ph.D. thesis, Instituto de Matemática e Estatistica, University of São Paulo, 2000
26. da Silva e Silva, P.J., Eckstein, J., Humes, C.: Rescaling and stepsize selection in proximal methods using separable generalized distances. SIAM J. Optim. 12, 238-261 (2001)
27. Solodov, M.V., Svaiter, B.F.: An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions. Math. Operations Res. 25, 214-230 (2000)
28. Teboulle, M.: Entropie proximal mappings with applications to nonlinear programming. Math. Operations Res. 17, 670-690 (1992)
29. Teboulle, M.: Convergence of proximal-like algorithms. SIAM J. Optim. 7, 1069-1083 (1997)
30. Tossings, P.: The perturbed proximal point algorithm and some of its applications. Appl. Math. Optim. 29, 125-159 (1994)
31. Tseng, P., Bertsekas, D.P.: On the convergence of the exponential multiplier method for convex programming. Math. Programming 60, 1-19 (1993)