Advertisement

Journal of Optimization Theory and Applications

, Volume 142, Issue 3, pp 493–499 | Cite as

Feasibility-Solvability Theorem for a Generalized System

  • R. Hu
  • Y. P. FangEmail author
Article

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.

Keywords

Generalized systems Strict feasibility Solvability Monotonicity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fan, K.: A minimax inequality and applications. In: Shisha, O. (ed.) Inequality III, pp. 103–113. Academic Press, San Diego (1972) Google Scholar
  2. 2.
    Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994) zbMATHMathSciNetGoogle Scholar
  3. 3.
    Chang, K.C.: Variational methods for non-differentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl. 80, 102–129 (1981) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Motreanu, D., Panagiotopoulos, P.D.: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Kluwer Academic, Dordrecht (1999) zbMATHGoogle Scholar
  5. 5.
    Bianchi, M., Schaible, S.: Generalized monotone bifunctions and equilibrium problems. J. Optim. Theory Appl. 90, 31–43 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bianchi, M., Hadjisavvas, N., Schaible, S.: Vector equilibrium problems with generalized monotone bifunctions. J. Optim. Theory Appl. 92, 527–542 (1997) zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hadjisavvas, N., Schaible, S.: From scalar to vector equilibrium problems in the quasimonotone case. J. Optim. Theory Appl. 96, 297–309 (1998) zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Oettli, W.: A remark on vector-valued equilibria and generalized monotonicity. Acta Math. Vietnam. 22, 213–221 (1997) zbMATHMathSciNetGoogle Scholar
  9. 9.
    Martínez-Legaz, J.E., Sosa, W.: Duality for equilibrium problems. J. Glob. Optim. 35, 311–319 (2006) zbMATHCrossRefGoogle Scholar
  10. 10.
    Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problems. Academic Press, San Diego (1992) Google Scholar
  11. 11.
    Isac, G.: Topological Methods in Complementarity Theory. Kluwer Academic, Dordrecht (2000) zbMATHGoogle Scholar
  12. 12.
    Fang, Y.P., Huang, N.J.: Equivalence of equilibrium problems and least element problems. J. Optim. Theory Appl. 132, 411–422 (2007) zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Baiocchi, C., Capelo, A.: Variational and Quasivariational Inequalities: Applications to Free Boundary Problems. Wiley, New York (1984) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsChengdu University of Information TechnologyChengduPeople’s Republic of China
  2. 2.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China

Personalised recommendations