Entropic proximal decomposition methods for convex programs and variational inequalities

Mathematical Programming, Series B

Volumn 91, Issue 1, 2001, Pages 33-47

  Auslander, Alfred ^a   Teboulle, Marc ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Convex optimization; Decomposition methods; Entropic interior proximal methods; Lagrangian multiplier methods; Variational inequalities

Indexed keywords

EID: 4043138107     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100241     Document Type: Article

References (25)

1. Auslender, A., Teboulle, M., Ben-Tiba, S. (1999): A logarithmic-quadratic proximal method for variational inequalities. Comput. Optim. Appl. 12, 31-40
2. Auslender, A., Teboulle, M., Ben-Tiba, S. (1999): Interior proximal and multiplier methods based on second order homogeneous kernels. Math. Oper. Res. 24, 645-668
3. Auslender, A., Teboulle, M. (2000): Lagrangian duality and related multiplier methods for variational inequalities. SIAM J. Optim. 10, 1097-1115
4. Bertsekas, D.P. (1982): Constrained optimization and Lagrangian multipliers. Academic Press, New York
5. Bertsekas, D.P., Tsitsiklis, J.N. (1989): Parallel and distributed computation: numerical methods. Prentice-Hall, New Jersey
6. Chen, G., Teboulle, M. (1994): A proximal based decomposition method for convex minimization problems. Math. Program. 64, 81-101
7. Eckstein, J., Bertsekas, D.P. (1992): On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293-318
8. Fortin, M., Glowinski, R. (1983): Augmented Lagrangian methods: applications to the solution of boundary-valued problems. North-Holland, Amsterdam
9. Fukushima, M. (1992): Application of the alternating direction method of multipliers to separable convex programming problems. Comput. Optim. Appl. 1, 93-111
10. Gabay, D. (1983): Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (ed.). Augmented Lagrangian methods: applications to the solution of boundary-valued problems. North-Holland, Amsterdam, pp. 299-331
11. Gabay, D., Mercier, B. (1976): A dual algorithm for the solution of nonlinear variational problems via finite-element approximations. Comput. Math. Appl. 2, 17-40
12. Glowinski, R., Le Tallec, P. (1989): Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. In: SIAM Studies in Applied Mathematics. SIAM, Philadelphia
13. Güler, O. (1991): On the convergence of the proximal point algorithm for convex minimization. SIAM J. Control Optim. 29, 403-419
14. Kyono, M., Fukushima, M. (1999): Nonlinear proximal decomposition methods for convex programming. Preprint, July 1999
15. Lions, P.L., Mercier, B. (1979): Splitting algorithms for the sum of two nonlinear operators. SIAM J. Numer. Anal. 16, 964-979
16. Martinet, B. (1970): Regularisation d'inéquations variationnelles par approximations successive. Revue Francaise d'Automatique et Informatique Recherche Opérationnelle 4, 154-159
17. Nesterov, Y., Nemirovski, A. (1994): Interior point polynomial algorithms in convex programming. SIAM Publications, Philadelphia, PA
18. Rockafellar, R.T. (1970): Convex Analysis. Princeton University Press, Princeton, NJ
19. Rockafellar, R.T. (1970): On the maximality of sums of nonlinear monotone operators. Trans. Am. Math. Soc. 149, 75-88
20. Rockafellar, R.T. (1976): Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877-898
21. Rockafellar, R.T. (1978): Monotone operators and augmented Lagrangians in nonlinear programming. In: Mangasarian, O.L., et al. (eds.), Nonlinear Programming 3. Academic Press, New York, pp. 1-25
22. Spingarn, J.E. (1985): Applications of the method of partial inverses to convex programming: decomposition. Math. Program. 32, 199-223
23. Tseng, P. (1991): Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM J. Control Optim. 29, 119-138
24. Tseng, P. (1997): Alternating projection-proximal methods for convex programming and variational inequalities. SIAM J. Optim. 7, 951-967
25. Uzawa, H. (1958): Iterative methods for concave programming. In: Arrow, K.J., Hurwicz, L., Uzawa, H. (eds.), Studies in Linear and Nonlinear Programming. Stanford University Press, Stanford, CA, pp. 154-165