An extragradient-type algorithm for non-smooth variational inequalities

Optimization

Volumn 48, Issue 3, 2000, Pages 309-332

  Iusem, Alfredo N ^a   Lucambio Pérez, Luis R ^b  

^a IMPA   (Brazil)

^b FEDERAL UNIVERSITY OF GOIÁS   (Brazil)

Author keywords

Extragradient type methods; Point to set operators; Variational inequalities

Indexed keywords

EID: 0242699761     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Alber, Y. I. (1983). Recurrence relations and variational inequalities. Soviet Mathematics, Doklady, 27, 511-517.
2. Bertsekas, D. (1982). Constrained Optimization and Lagrange Multipliers. Academic Press, New York.
3. Burachik, R. and Iusem, A. N. (1998). A generalized proximal point algorithm for the variational inequality problem in a Hilbert space. SIAM Journal on Optimization, 8.
4. Burachik, R., Iusem, A. N. and Svaiter, B. F. (1997). Enlargement of monotone operators with applications to variational inequalities. Technical Report B-110, IMPA, Rio de Janeiro.
5. Burachik, R., Iusem, A. N. and Svaiter, B. F. (1997). Enlargement of monotone operators with applications to variational inequalities. Set-Valued Analysis, 5, 159-180.
6. Goffin, J.-L., Marcotte, P. and Zhu, D. L. (1997). An analytic center cutting plane method for pseudomonotone variational inequalities. Operations Research Letters, 20, 1-6.
7. Hiriart-Urruty, J.-B. and Lemaréchal, C. (1993). Convex Analysis and Minimization Algorithms, Volume I. Springer-Verlag, Berlin.
8. Iusem, A. N. (1994). An iterative algorithm for the variational inequality problem. Computational and Applied Mathematics, 13, 103-114.
9. Iusem, A. N. and Svaiter, B. F. (1997). A variant of Korpelevich's method for variational inequalities with a new search strategy. Optimization, 42, 309-321.
10. Khobotov, E. N. (1987). Modifications of the extragradient method for solving variational inequalities and certain optimization problems. USSR Computational Mathematics and Mathematical Physics, 27, 120-127.
11. Korpelevich, G. M. (1976). The extragradient method for finding saddle points and other problems. Ekonomika i Matematcheskie Metody, 12, 747-756.
12. Lucambio Pérez, L. R. (1997). Iterative Algorithms for non-smooth variational inequalities. Ph.D. Thesis, Instituto de Mathemática Pura e Aplicada, Rio de Janeiro.
13. Marcotte, P. (1991). Application of Khobotov's algorithm to variational inequalities and network equilibrium problems. Information Systems and Operational Research, 29, 258-270.
14. Marcotte, P. and Zhu, D. L. (1996). Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM Journal on Optimization, 6, 714-726.
15. Nguyen, S. and Dupuis, C. (1984). An efficient method for computing traffic equilibria in networks with asymmetric transportation costs. Transportation Science, 18, 185-202.
16. Solodov, M. V. and Tseng, P. (1996). Modified projection-type methods for monotone variational inequalities. SIAM Journal on Control and Optimization, 34, 1814-1830.
17. Solodov, M. V. and Svaiter, B. F., A new projection method for monotone variational inequality problems (to be published in SIAM Journal on Control and Optimization).