Optimization Letters

, Volume 4, Issue 1, pp 57–66 | Cite as

A note on duality of generalized equilibrium problem

Original Paper


The main aim of this note is to extend the dual (in the form of an optimization problem) given for equilibrium problem by Martinez-Legaz and Sosa (in J Glob Optim 35:311–319, 2006) for a generalized equilibrium problem in finite dimensional setting and to establish its equivalence with the dual derived by Bigi et al. (in J Math Anal Appl 342:17–26, 2008) (in the form of inclusion conditions) under a mild condition.


Equilibrium problems Duality Conjugate function Subdifferential 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bigi G., Castellani M., Kassay G.: A dual view of equilibrium problems. J. Math. Anal. Appl. 342, 17–26 (2008)MATHMathSciNetGoogle Scholar
  2. 2.
    Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problems. Math. Student. 63, 123–145 (1994)MATHMathSciNetGoogle Scholar
  3. 3.
    Chinchuluun A., Pardalos P.M., Migdalas A., Pitsoulis L.: Pareto Optimality, Game Theory and Equilibria. Springer, New York (2008)MATHCrossRefGoogle Scholar
  4. 4.
    Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequalities. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  5. 5.
    Iusem A.N., Sosa W.: New existence results for equilibrium problems. Nonlinear Anal. 52, 621–635 (2003)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jacinto F.M.O., Scheimberg S.: Duality for generalized equilibrium problem. Optimization 57, 795–805 (2008)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Konnov I.V., Schaible S.: Duality for equilibrium problems under generalized monotonicity. J. Optim. Theory Appl. 104, 395–408 (2002)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Martínez-Legaz J.E., Sosa W.: Duality for equilibrium problems. J. Glob. Optim. 35, 311–319 (2006)MATHCrossRefGoogle Scholar
  9. 9.
    Mosco U.: Dual variational inequalities. J. Math. Anal. Appl. 40, 202–206 (1972)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsDelhi University South CampusNew DelhiIndia

Personalised recommendations