Convergence of a splitting inertial proximal method for monotone operators

Journal of Computational and Applied Mathematics

Volumn 155, Issue 2, 2003, Pages 447-454

  Moudafi, A ^a   Oliny, M ^a  

^a UNIVERSITÉ DES ANTILLES ET DE LA GUYANE   (France)

Author keywords

Cocoercivity; Convergence; Enlargements; Monotone operators; Projection; Proximal point algorithm; Splitting algorithm

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

MONOTONE OPERATORS;

CONVERGENCE OF NUMERICAL METHODS;

MATHEMATICAL METHOD;

EID: 0037532448     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00906-8     Document Type: Article

References (25)

1. Alvarez F. On the minimizing property of a second order dissipative system in Hilbert space SIAM J. Control Optim. 38 4 2000 1102-1119.
2. Alvarez F. Attouch H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping Set Valued Anal. 9 2001 3-11.
3. A.S. Antipin, Continuous and iterative process with projection operators and projection-like operators, Voprosy Kibernetiki. Vychislitel'nye Voprosy Analiza Bol'shikh Sistem, AN SSSR, Scientific Counsel on the Complex Problem "Cybernetics", Moscow, 1989, pp. 5-43.
4. Attouch H. Goudou X. Redont P. The heavy ball with friction. I. The continuous dynamical system Comm. Contemp. Math. 2 1 2000 1-34.
5. Bertsekas D.P. Constrained Optimization and Lagrange Multiplier Methods 1982 Academic Press New York.
6. Chen H.-G. Rockafellar R.T. Convergence rates in forward-backward splitting SIAM J. Optim. 7 1997 421-444.
7. J. Ekstein, Splitting methods for monotone operators with application to parallel optimization, Dissertation, Massachussets Institute of Technology, 1989.
8. Ekstein J. Bertsekas D.P. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators Math. Programming 55 1992 293-318.
9. Gabay D. Applications of the method of multipliers to variational inequalities Fortin M. Glowinski R. Augmented Lagrangian Methods: Applications to the numerical solution of Boundary Value Problems 1983 299-331 North-Holland Amsterdam.
10. Han S.P. Lou G. A parallel algorithm for a class of convex programs SIAM J. Control Optim. 26 1988 345-355.
11. F. Jules, P.E. Maingé, Numerical approach to a stationary solution of a second order dissipative dynamical system, Optimization, to appear.
12. Lions P.L. Mercier B. Splitting algorithms for the sum of two nonlinear operators SIAM J. Numer. Anal. 16 1979 964-979.
13. B. Martinet, Régularisation d'inéquations variationnelles par approximations successives, Rev. Francaise Inf. Rech. Oper. R-3 (1970) 154-159.
14. B. Mercier, Inéquations variationnelles de la mécanique, Pub. Math. Orsay, 80.01, Université de Paris-Sud, Orsay, 1980.
15. Moudafi A. Thaéra M. Finding a zero of the sum of two maximal monotone operators J. Optim. Theory Appl. 94 1997 425-448.
16. Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings Bull. Amer. Math. Soc. 73 1967 591-597.
17. Passty G.B. Ergodic convergence to a zero of the sum of monotone operators in Hilbert spaces J. Math. Anal. Appl. 72 1979 383-390.
18. Polyak B.T. Some methods of speeding up the convergence of iterative methods Zh. Vychisl. Mat. Mat. Fiz. 4 1964 1-17.
19. Rockafellar R.T. Monotone operator and the proximal point algorithm SIAM J. Control. Opt. 14 5 1976 877-898.
20. Sibony M. Méthodes itératives pour leséquations et inéquations non linéaires de type monotone Calcolo 7 1970 65-183.
21. Svaiter B.F. Burachik R.S. Iusem A.N. Enlargement of maximal monotone operators with application to variational inequalities Set-Valued Anal. 5 1997 159-180.
22. Svaiter B.F. Burachik R.S. ε-enlargements of maximal monotone operators in Banach spaces Set-Valued Anal. 7 1999 117-132.
23. Tseng P. Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming Math. Programming 48 1990 249-263.
24. Tseng P. Applications of a splitting algorithm to decomposition in convex programming and variational inequalities SIAM J. Control Optim. 29 1991 119-138.
25. Zhu D.L. Marcotte P. Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities SIAM J. Optim. 9 3 1996 714-726.