Application of the proximal point method to nonmonotone equilibrium problems

Journal of Optimization Theory and Applications

Volumn 119, Issue 2, 2003, Pages 317-333

  Konnov, I V ^a  

^a KAZAN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Equilibrium problems; Nonmonotone bifunctions; Proximal point methods

Indexed keywords

BIFUNCTIONS; CONSTRAINED PROBLEM; CONVEX SET; DUAL PROBLEM; EQUILIBRIUM PROBLEM; GENERAL EQUILIBRIUM; NONMONOTONE; NONMONOTONE BIFUNCTION; PROXIMAL POINT METHOD;

SET THEORY;

EID: 0344583837     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTA.0000005448.12716.24     Document Type: Article

References (15)

1. MARTINET, B., Regularization d'Inéquations Variationnelles par Approximations Successives, Revue Française d'Informatique et de Recherche Opérationelle, Vol. 4, pp. 154-159, 1970.
2. ROCKAFELLAR, R. T., Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, Vol. 14, pp. 877-898, 1976.
3. ECKSTEIN, J., and BERTSEKAS, D. P., On the Douglas-Rachford Splitting Method and the Proximal Point Algorithm for Maximal Monotone Operators, Mathematical Programming, Vol. 55, pp. 293-318, 1992.
4. GOL'SHTEIN, E. G., and TRET'YAKOV, N. V., Modified Lagrangians and Monotore Maps in Optimization, John Wiley and Sons, New York, NY, 1996.
5. PATRIKSSON, M., Nonlinear Programming and Variational Inequality Problems: A Unified Approach, Kluwer Academic Publishers, Dordrecht, Netherlands, 1999.
6. BILLUPS, S. C., and FERRIS, M. C., QPCOMP: A Quadratic Programming Based Solver for Mixed Complementarity Problems, Mathematical Programming, Vol. 76, pp. 533-562, 1997.
7. BAIOCCHI, C., and CAPELO, A., Variational and Quasivariational Inequalities: Applications to Free Boundary Problems, John Wiley and Sons, New York, NY, 1984.
8. BLUM, E., and OETTLI, W., From Optimization and Variational Inequalities to Equilibrium Problems, Mathematics Student, Vol. 63, pp. 123-145, 1994.
9. HADJISAVVAS, N., and SCHAIBLE, S., Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems, Generalized Convexity, Generalized Monotonicity, Edited by J. P. Crouzeix, J. E. Martinez-Legaz, and M. Volle, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 257-275, 1998.
10. KONNOV, I. V., and SCHAIBLE, S., Duality for Equilibrium Problems under Generalized Monotonicity, Journal of Optimization Theory and Applications, Vol. 104, pp. 395-408, 2000.
11. EL FAROUQ, N., Pseudomonotone Variational Inequalities: Convergence of Proximal Methods, Journal of Optimization Theory and Applications, Vol. 109, pp. 311-326, 2001.
12. KONNOV, I. V., Combined Relaxation Methods for Variational Inequalities, Springer Verlag, Berlin, Germany, 2001.
13. NIKAIDO, H., Convex Structures and Economic Theory, Academic Press, New York, NY, 1968.
14. CHEN, G. Y., GOH, C. J., and YANG, X. Q., On Gap Functions and Duality of Variational Inequality Problems, Journal of Mathematical Analysis and Applications, Vol. 214, pp. 658-673, 1997.
15. KONNOV, I. V., Approximate Methods for Primal-Dual Mixed Variational Inequalities, Russian Mathematics (Izvestiya VUZ), Vol. 44, pp. 55-66, 2000.