A new inexact alternating directions method for monotone variational inequalities

Mathematical Programming, Series B

Volumn 92, Issue 1, 2002, Pages 103-118

  He, Bingsheng ^a   Liao, Li Zhi ^b   Han, Deren ^a   Yang, Hai ^c  

^a NANJING UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Alternating directions method; Inexact method; Variational inequality

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

ALTERNATING DIRECTIONS METHODS; INEXACT METHODS; PARAMETER CONDITIONS; VARIATIONAL INEQUALITIES;

COMPUTATIONAL METHODS;

EID: 0242462717     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100280     Document Type: Article

References (28)

1. Bertsekas, D.P., Gafni, E. M. (1982): Projection method for variational inequalities with applications to the traffic assignment problem. Mathematical Programming Study 17, 139-159
2. Burachik, R.S., Scheimberg, S., Svaiter, B.F. (1999): Robustness of the extragradient-proximal point algorithm. Working Paper, Instituto de Mathematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil
3. Chen, G., Teboulle, M. (1994): A proximal-based decomposition method for convex minimization problems. Mathematical Programming 64, 81-101
4. Dafermos, S. (1980): Traffic equilibrium and variational inequalities. Transportation Science 14, 42-54
5. Drezner, Z. (ed.) (1995): Facility Location: A survey of applications and methods. Springer-Verlag, New York
6. Eaves, B.C. (1971): On the basic theorem of complementarity. Mathematical Programming 1, 68-75
7. Eckstein, J. (1994): Some saddle-function splitting methods for convex programming. Optimization Methods and Software 4, 75-83
8. Eckstein, J., Bertsekas, D.P. (1992): On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming 55, 293-318
9. Eckstein, J., Fukushima, M. (1994): Some reformulation and applications of the alternating directions method of multipliers. In: Hager, W.W. et al., eds., Large Scale Optimization: State of the Art, pp. 115-134. Kluwer Academic Publishers
10. Fortin, M., Glowinski, R. (Eds.) (1983): Augmented Lagrangian methods: Applications to the numerical solution of Boundary-Value Problems. North-Holland, Amsterdam
11. Fukushima, M. (1992): Application of the alternating directions method of multipliers to separable convex programming problems. Computational Optimization and Applications 2, 93-111
12. Gabay, D. (1983): Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R., eds., Augmented Lagrangian methods: Applications to the numerical solution of Boundary-Value Problems, pp. 299-331. North-Holland, Amsterdam, The Netherlands
13. Gabay, D., Mercier, B. (1976): A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Computer and Mathematics with Applications 2, 17-40
14. Glowinski, R. (1984): Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York
15. Glowinski, R., Le Tallec, P. (1989): Augmented Lagrangian and Operator-Splitting Methods. In: Nonlinear Mechanics, SIAM Studies in Applied Mathematics, Philadelphia, PA
16. Harker, P.T., Pang, J.S. (1990): Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and Applications. Mathematical Programming 48, 161-220
17. He, B.S. (1997):. A class of new methods for monotone variational inequalities. Applied Mathematics and Optimization 35, 69-76
18. He, B.S. (1999): Inexact implicit methods for monotone general variational inequalities. Mathematical Programming 86, 199-217
19. He, B.S., Yang, H. (1998): Some convergence properties of a method of multipliers for linearly constrained monotone variational inequalities. Operations Research Letters 23, 151-161
20. Kontogiorgis, S., Meyer, R.R. (1998): A variable-penalty alternating directions method for convex optimization. Mathematical Programming 83, 29-53
21. Nagurney, A. (1993): Network economics, A variational inequality approach. Kluwer Academics Publishers, Dordrecht
22. Nagurney, A., Ramanujam, P. (1996): Transportation network policy modeling with goal targets and generalized penalty functions. Transportation Science 30, 3-13
23. Nagurney, A., Thore, S., Pan, J. (1996): Spatial market policy modeling with goal targets. Operations Research 44, 393-406
24. Rockafellar, R.T. (1976): Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Mathematics of Operations Research 1, 97-116
25. Solodov, M., Svaiter, B.F. (1999): A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator. Set-Valued Analysis 7, 117-132
26. Taji, K., Fukushima, M., Ibaraki, T. (1993): A globally convergent Newton method for solving strongly monotone variational inequalities. Mathematical Programming 58, 369-383
27. Tseng, P. (1991): Applications of a splitting algorithm to decomposition in convex programming and variational inequalities. SIAM J. Control and Optimization 29, 119-138
28. Tseng, P. (1997): Alternating projection-proximal methods for convex programming and variational inequalities. SIAM J. Optimization 7, 951-965