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On maximal monotonicity of bifunctions on Hadamard manifolds

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Abstract

We study some conditions for a monotone bifunction to be maximally monotone by using a corresponding vector field associated to the bifunction and vice versa. This approach allows us to establish existence of solutions to equilibrium problems in Hadamard manifolds obtained by perturbing the equilibrium bifunction.

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Acknowledgements

The research of the first author was supported in part by CNPq grant 305462/2014-8. The research of the second author was supported in part by CAPES/FAPEAM grant 062.01818/2015 and CAPES grant 88881.123555/2016-01. The authors wish to express their gratitude to the anonymous referees for their helpful comments.

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Authors and Affiliations

  1. CCN, DM, Universidade Federal do Piauí, Teresina, Brazil

    J. X. Cruz Neto & J. C. O. Souza

  2. DM, Universidade Federal do Amazonas, Manaus, Brazil

    F. M. O. Jacinto

  3. DM, Universidade Estadual do Piauí, Teresina, Brazil

    P. A. Soares Jr

Authors
  1. J. X. Cruz Neto
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  2. F. M. O. Jacinto
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  3. P. A. Soares Jr
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  4. J. C. O. Souza
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Correspondence to J. C. O. Souza.

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Cruz Neto, J.X., Jacinto, F.M.O., Soares, P.A. et al. On maximal monotonicity of bifunctions on Hadamard manifolds. J Glob Optim 72, 591–601 (2018). https://doi.org/10.1007/s10898-018-0663-9

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  • DOI: https://doi.org/10.1007/s10898-018-0663-9

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