Optimization Letters

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

A note on duality of generalized equilibrium problem

  • C. S. Lalitha
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