New existence results for equilibrium problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 2, 2003, Pages 621-635

  Iusem, Alfredo N ^a   Sosa, Wilfredo ^b  

^a IMPA   (Brazil)

^b PUCP   (Peru)

Author keywords

Convex feasibility problems; Convex optimization; Equilibrium problems; Variational inequalities

Indexed keywords

FUNCTIONS; OPTIMIZATION; SET THEORY; VECTORS;

EQUILIBRIUM PROBLEMS;

PROBLEM SOLVING;

EID: 0037209766     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00154-2     Document Type: Article

References (19)

1. Allen G. Variational inequalities, complementarity problems and duality theorems. J. Math. Anal. Appl. 58:1977;1-10.
2. Auslender A. Noncoercive optimization problems. Math. Oper. Res. 21:1996;769-782.
3. Auslender A. Résolution numérique d'inégalités variatonnelles. RAIRO. R2:1973;67-72.
4. Baiocchi C., Buttazo G., Gastaldi F., Tomarelli F. General existence theorem for unilateral problems in continuum mechanics. Arch. Rational Mech. Anal. 100:1988;149-189.
5. Berge C. Espaces Topologiques et Fonctions Multivoques. 1959;Dunod, Paris.
6. Bianchi M., Schaible S. Generalized monotone bifunctions and equilibrium problems. J. Optim. Theory Appl. 90:1996;31-43.
7. Blum E., Oettli W. From optimization and variational inequalities to equilibrium problems. Math. Student. 63:1994;123-145.
8. Brezis H., Nirenberg L., Stampacchia G. A remark on Ky Fan's minimax principle. Boll. Un. Mat. Ital. 6:1972;293-300.
9. Crouzeix J.P. Pseudomonotone variational inequality problems. existence of solutions Math. Programming. 78:1997;305-314.
10. Fan K. A generalization of Tychonoff's fixed point theorem. Math. Ann. 142:1961;305-310.
11. Fan K. A minimax inequality and applications. Shisha O. Inequality III. 1972;103-113 Academic Press, New York.
12. L.M. Graña Drummond, personal communication.
13. Hiriart-Urruty J.-B., Lemaréchal C. Convex Analysis and Minimization Algorithms. 1993;Springer, Berlin.
14. Karamardian S., Schaible S. Seven kinds of monotone maps. J. Optim. Theory Appl. 66:1990;37-46.
15. Muu L.D., Oettli W. Convergence of an adaptive penalty scheme for finding constraint equilibria. Nonlinear Anal. Theory Methods Appl. 18:1992;1159-1166.
16. Oettli W. A remark on vector-valued equilibria and generalized monotonicity. Acta Math. Vietnam. 22:1997;215-221.
17. W. Oettli, D. Schläger, Generalized vectorial equilibrium and generalized monotonicity, Funct. Anal. Appl., Pitman Res. Notes Maths. Ser. 377 (1998) 145-154.
18. Van Tiel J. Convex Analysis, An Introductory Text. 1984;Wiley, New York.
19. Yen C. A minimax inequality and its application to variational inequalities. Pacific J. Math. 97:1981;477-481.