A proximal point method for the variational inequality problem in Banach spaces

SIAM Journal on Control and Optimization

Volumn 39, Issue 5, 2001, Pages 1633-1649

  Burachik, R S ^a   Scheimberg, S ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Algorithmic scheme; Banach spaces; Convergence; Maximal monotone operators; Proximal point algorithm

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL OPERATORS; VARIATIONAL TECHNIQUES;

BANACH SPACES; PROXIMAL POINT METHODS; VARIATIONAL INEQUALITY;

SET THEORY;

EID: 0034769650     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012998339745     Document Type: Article

References (44)

1. Application of the mesh independence principle to mesh refinement strategies
2. A mesh independence principle for operator equations and their discretizations
3. Legendre Functions and the method of random Bregman functions
4. The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming
5. Image d'une somme d'opérateurs monotones et applications
6. Nonlinear operators and nonlinear equations of evolution in Banach spaces
7. Iterative averaging of entropic projections for solving stochastic convex feasibility problems
8. Strong convergence of expected projection methods in Hilbert spaces
9. A generalized proximal point algorithm for the variational inequality problem in a Hilbert space
10. Local moduli of convexity and their applications to finding almost common points of measurable families of operators
11. On a proximal point method for convex optimization in Banach spaces
12. Total convexity of powers of the norm in uniformly convex Banach spaces
13. Iterative methods for solving stochastic convex feasibility problems and applications
14. A mixed Hölder and Minkowski inequality
15. Nonexpansive projections and resolvents of accretive operators in Banach spaces
16. An interior point method with Bregman functions for the variational inequality problem with paramonotone operators
17. An iterative row-action method for interval convex programming
18. On iterative methods for linearly constrained entropy maximization
19. The proximal minimization algorithm with D-functions
20. Convergence analysis of a proximal-like optimization algorithm using Bregman functions
21. A relaxed version of Bregman's method for convex programming
22. Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
23. Applications of the method of multipliers to variational inequalities
24. Mesh independence for nonlinear least squares problems with norm constraints
25. On some properties of paramonotone operators
26. On some properties of generalized proximal point methods for quadratic and linear programming
27. Complementarity problems over cones with monotone and pseudomonotone maps
28. Mesh independence of Newton-like methods for infinite dimensional problems
29. Free-steering relaxation methods for problems with strictly convex costs and linear constraints
30. Proximal minimization methods with generalized Bregman functions
31. Newton's mesh independence principle for a class of optimal shape design problems
32. Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces
33. The range of sums of accretive and monotone operators
34. A weak convergence theorem for the alternating method with Bregman distances
35. Local boundedness of nonlinear monotone operators
36. On the maximality of sums of nonlinear monotone operators
37. Monotone operators and the proximal point algorithm
38. Augmented Lagrangians and applications to the proximal point algorithm in convex programming