Abstract
In this paper, we consider a generalized system in the framework of the formulation proposed by Blum and Oettli. The concepts of feasibility and strict feasibility are introduced for a generalized system and a feasibility-solvability theorem is obtained.
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Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequality III, pp. 103–113. Academic Press, San Diego (1972)
Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994)
Chang, K.C.: Variational methods for non-differentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80, 102–129 (1981)
Motreanu, D., Panagiotopoulos, P.D.: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Kluwer Academic, Dordrecht (1999)
Bianchi, M., Schaible, S.: Generalized monotone bifunctions and equilibrium problems. J. Optim. Theory Appl. 90, 31–43 (1996)
Bianchi, M., Hadjisavvas, N., Schaible, S.: Vector equilibrium problems with generalized monotone bifunctions. J. Optim. Theory Appl. 92, 527–542 (1997)
Hadjisavvas, N., Schaible, S.: From scalar to vector equilibrium problems in the quasimonotone case. J. Optim. Theory Appl. 96, 297–309 (1998)
Oettli, W.: A remark on vector-valued equilibria and generalized monotonicity. Acta Math. Vietnam. 22, 213–221 (1997)
Martínez-Legaz, J.E., Sosa, W.: Duality for equilibrium problems. J. Glob. Optim. 35, 311–319 (2006)
Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problems. Academic Press, San Diego (1992)
Isac, G.: Topological Methods in Complementarity Theory. Kluwer Academic, Dordrecht (2000)
Fang, Y.P., Huang, N.J.: Equivalence of equilibrium problems and least element problems. J. Optim. Theory Appl. 132, 411–422 (2007)
Baiocchi, C., Capelo, A.: Variational and Quasivariational Inequalities: Applications to Free Boundary Problems. Wiley, New York (1984)
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Communicated by F. Giannessi.
This work was supported by the Foundation for Young Teacher in Sichuan University (07069), the National Natural Science Foundation of China (10826064, 10671135) and the Specialized Research Fund for the Doctoral Program of Higher Education (20060610005). The authors thank Professor L.D. Muu (Hanoi) and the referee for valuable comments and suggestions which lead to improvements of this paper.
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Hu, R., Fang, Y.P. Feasibility-Solvability Theorem for a Generalized System. J Optim Theory Appl 142, 493–499 (2009). https://doi.org/10.1007/s10957-009-9510-y
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DOI: https://doi.org/10.1007/s10957-009-9510-y