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A note on duality of generalized equilibrium problem

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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.

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References

  1. Bigi G., Castellani M., Kassay G.: A dual view of equilibrium problems. J. Math. Anal. Appl. 342, 17–26 (2008)

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  3. Chinchuluun A., Pardalos P.M., Migdalas A., Pitsoulis L.: Pareto Optimality, Game Theory and Equilibria. Springer, New York (2008)

    Book  MATH  Google Scholar 

  4. Giannessi F., Maugeri A., Pardalos P.M.: Equilibrium Problems: Nonsmooth Optimization and Variational Inequalities. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  5. Iusem A.N., Sosa W.: New existence results for equilibrium problems. Nonlinear Anal. 52, 621–635 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Jacinto F.M.O., Scheimberg S.: Duality for generalized equilibrium problem. Optimization 57, 795–805 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Konnov I.V., Schaible S.: Duality for equilibrium problems under generalized monotonicity. J. Optim. Theory Appl. 104, 395–408 (2002)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Mosco U.: Dual variational inequalities. J. Math. Anal. Appl. 40, 202–206 (1972)

    Article  MATH  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Delhi University South Campus, Benito Jaurez Road, New Delhi, 110021, India

    C. S. Lalitha

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  1. C. S. Lalitha
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Lalitha, C.S. A note on duality of generalized equilibrium problem. Optim Lett 4, 57–66 (2010). https://doi.org/10.1007/s11590-009-0145-6

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  • DOI: https://doi.org/10.1007/s11590-009-0145-6

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