A hybrid inertial projection-proximal method for variational inequalities

Journal of Inequalities in Pure and Applied Mathematics

Volumn 5, Issue 3, 2004, Pages 1-5

  Moudafi, A ^a  

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

Author keywords

Hybrid projection proximal method; Inertial proximal point scheme; Maximal monotone operators; Proximal point algorithm; Resolvent; Weak convergence

Indexed keywords

EID: 4644233276     PISSN: 14435756     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. F. ALVAREZ, On the minimizing property of a second order dissipative system in Hilbert space, SIAM J. of Control and Optim., 14(38) (2000), 1102-1119.
2. F. ALVAREZ AND H. ATTOUCH, An inertial proximal method for maximal monotone operators via discretization of a non linear oscillator with damping, Set Valued Analysis, 9 (2001), 3-11.
3. H. BRÉZIS, Opérateurs maximaux monotones et semi-groupes des contractions dans les espaces de Hilbert, North Holland, Amsterdam, 1973.
4. B. MARTINET, Algorithmes pour la résolution des problèmes d'optimisation et de minmax, Thèse d'état Université de Grenoble, France (1972).
5. A. MOUDAFI AND M. OLINY, Convergence of a splitting inertial proximal method for monotone operators, Journal of Computational and Applied Mathematics, 155 (2003), 447-454.
6. A. MOUDAFI AND E. ELISABETH, Approximate inertial proximal methods using the enlargement of maximal monotone operators, International Journal of Pure and Applied Mathematics, 5(3) (2003), 283-299.
7. Z. OPIAL,Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bulletin of the American Mathematical Society, 73 (1967), 591-597.
8. R.T. ROCKAFELLAR, Monotone operator and the proximal point algorithm, SIAM J. Control. Optimization, 14(5) (1976), 877-898.
9. M.V. SOLODOV AND B.F. SVAITER, A hybrid projection-proximal point algorithm, Journal of Convex Analysis, 6(1) (1999), 59-70.
10. M.V. SOLODOV AND B.F. SVAITER, An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions, Mathematics of Operations Research, to appear.