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On Equivalent Equilibrium Problems

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Abstract

We give sufficient conditions for the equivalence between two equilibrium problems. In particular we deduce that, under suitable assumptions, an equilibrium problem has an equivalent reformulation as a generalized variational inequality. Such conditions are satisfied when the equilibrium bifunction is lower semicontinuous, coercive and quasiconvex with respect to the second variable. We also show that the equivalent generalized variational inequality inherits the same generalized monotonicity properties of the original nonconvex equilibrium problem.

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Authors and Affiliations

  1. Department S.I.E., University of L’Aquila, 67100, L’Aquila, Italy

    M. Castellani & M. Giuli

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  1. M. Castellani
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  2. M. Giuli
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Correspondence to M. Castellani.

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Communicated by F. Giannessi.

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Castellani, M., Giuli, M. On Equivalent Equilibrium Problems. J Optim Theory Appl 147, 157–168 (2010). https://doi.org/10.1007/s10957-010-9703-4

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  • DOI: https://doi.org/10.1007/s10957-010-9703-4

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