On the generalized vector variational inequality problem

Journal of Mathematical Analysis and Applications

Volumn 206, Issue 1, 1997, Pages 42-58

  Konnov, I V ^a   Yao, J C ^b  

^a KAZAN STATE UNIVERSITY   (Russian Federation)

^b NATIONAL SUN YAT SEN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; MATHEMATICAL OPERATORS; SET THEORY; VARIATIONAL TECHNIQUES;

BANACH SPACE; FAN LEMMA; PSEUDOMONOTONE MAPPING; VECTOR VARIATIONAL INEQUALITIES;

VECTORS;

EID: 0031060740     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5192     Document Type: Article

References (19)

1. 1. F. Giannessi, Theory of alternative, quadratic programs and complementarity problems, in "Variational Inequalities and Complementarity Problems" (R. W. Cottle, F. Giannessi, and J. L. Lions, Eds.), pp. 151-186, Wiley, New York, 1980.
2. 2. G. Y. Chen and X. Q. Yang, Vector complementarity problem and its equivalences with weak minimal element in ordered spaces, J. Math. Anal. Appl. 153 (1990), 136-158.
3. 3. G. Y. Chen and G. M. Cheng, Vector variational inequality and vector optimization, in "Lecture Notes in Economics and Mathematical Systems," Vol. 258, pp. 408-416, Springer-Verlag, Heidelberg, 1987.
4. 4. G. Y. Chen and B. D. Craven, A vector variational inequality and optimization over an efficient set, Z. Oper. Res. 3 (1990), 1-12.
5. 5. G. Y. Chen, Existence of solution for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem, J. Optim. Theory Appl. 74 (1992), 445-456.
6. 6. X. Q. Yang, Vector variational inequality and its duality, Nonlinear Anal. 21 (1993), 869-877.
7. 7. S. J. Yu and J. C. Yao, On vector variational inequalities, J. Optim. Theory Appl. 89 (1996), 749-769.
8. 8. K. L. Lin, D. P. Yang, and J. C. Yao, Generalized vector variational inequalities, J. Optim. Theory Appl. 92 (1997).
9. 9. S. C. Fang and E. L. Petersen, Generalized variational inequalities, J. Optim. Theory Appl. 38 (1982), 363-383.
10. 10. K. Fan, A generalization of Tychonoff's fixed-point theorem, Math. Ann. 142 (1961), 305-310.
11. 11. B. Knaster, C. Kuratowski, and S. Mazurkiewicz, Ein Beweis des Fixpunktsatzes für N Dimensionale Simplexe, Fund. Math. 14 (1929), 132-137.
12. 12. S. Karamadian, Complementarity over cones with monotone and pseudomonotone maps, J. Optim. Theory Appl. 18 (1976), 445-454.
13. 13. G. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341-346.
14. 14. J. B. Conway, "A Course in Functional Analysis," 2nd ed., Springer-Verlag, New York, 1990.
15. 15. J. C. Yao, Multi-valued variational inequalities with K-pseudomonotone operators, J. Optim. Theory Appl. 83 (1994), 391-403.
16. 16. A. Daniilidis and N. Hadjisavvas, Variational inequalities with quasimonotone multivalued operators, preprint.
17. 17. H. Kneser, Sur le Théorème Fondamentale de al Théorie des Jeux, C. R. Acad. Sci. Paris 234 (1952), 2418-2420.
18. 18. I. V. Konnov, Combined relaxation methods for finding equilibrium points and solving related problems, Izv. Vyssh. Uchebn. Zaved. Mat. 37 (1993), 44-51.
19. 19. I. V. Konnov, On combined relaxation methods' convergence rates, Izv. Vyssh. Uchebn. Zaved. Mat. 37 (1993), 89-92.