Skip to main content
SpringerLink
Log in

Feasibility-Solvability Theorem for a Generalized System

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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. Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123–145 (1994)

    MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  4. Motreanu, D., Panagiotopoulos, P.D.: Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Kluwer Academic, Dordrecht (1999)

    MATH  Google Scholar 

  5. Bianchi, M., Schaible, S.: Generalized monotone bifunctions and equilibrium problems. J. Optim. Theory Appl. 90, 31–43 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bianchi, M., Hadjisavvas, N., Schaible, S.: Vector equilibrium problems with generalized monotone bifunctions. J. Optim. Theory Appl. 92, 527–542 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hadjisavvas, N., Schaible, S.: From scalar to vector equilibrium problems in the quasimonotone case. J. Optim. Theory Appl. 96, 297–309 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Oettli, W.: A remark on vector-valued equilibria and generalized monotonicity. Acta Math. Vietnam. 22, 213–221 (1997)

    MATH  MathSciNet  Google Scholar 

  9. Martínez-Legaz, J.E., Sosa, W.: Duality for equilibrium problems. J. Glob. Optim. 35, 311–319 (2006)

    Article  MATH  Google Scholar 

  10. Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problems. Academic Press, San Diego (1992)

    Google Scholar 

  11. Isac, G.: Topological Methods in Complementarity Theory. Kluwer Academic, Dordrecht (2000)

    MATH  Google Scholar 

  12. Fang, Y.P., Huang, N.J.: Equivalence of equilibrium problems and least element problems. J. Optim. Theory Appl. 132, 411–422 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Baiocchi, C., Capelo, A.: Variational and Quasivariational Inequalities: Applications to Free Boundary Problems. Wiley, New York (1984)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Chengdu University of Information Technology, Chengdu, Sichuan, People’s Republic of China

    R. Hu

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    Y. P. Fang

Authors
  1. R. Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. P. Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. P. Fang.

Additional information

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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-009-9510-y

Keywords

Search

Navigation