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On a Bregman regularized proximal point method for solving equilibrium problems

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Abstract

In this paper, we propose a Bregman regularized proximal point method for solving monotone equilibrium problems. Existence and uniqueness results as well as convergence of the sequence to a solution of an equilibrium problem is analyzed. We assume a coercivity condition on the Bregman function weaker than the one considered in the literature on equilibrium problems with Bregman regularization. Numerical experiments illustrate the efficiency of the method.

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Acknowledgements

The work of the first author was supported in part by CNPq Grant 305462/2014-8. The work of the second author was supported in part by CNPq Grant 303368/2016-0. The work of the third author was supported in part by CAPES Grant 88881.123555/2016-01 and CAPES/FAPEAM Grant 062.01818/2015.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Piauí, Teresina, PI, Brazil

    J. X. Cruz Neto

  2. CMRV, Federal University of Piauí, Parnaíba, PI, Brazil

    P. S. M. Santos

  3. Department of Mathematics, Federal University of Amazonas, Manaus, AM, Brazil

    R. C. M. Silva

  4. Department of Mathematics, Federal University of Piauí, Teresina, PI, Brazil

    J. C. O. Souza

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  1. J. X. Cruz Neto
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  2. P. S. M. Santos
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  3. R. C. M. Silva
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  4. J. C. O. Souza
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Correspondence to R. C. M. Silva.

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Neto, J.X.C., Santos, P.S.M., Silva, R.C.M. et al. On a Bregman regularized proximal point method for solving equilibrium problems. Optim Lett 13, 1143–1155 (2019). https://doi.org/10.1007/s11590-019-01411-2

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  • DOI: https://doi.org/10.1007/s11590-019-01411-2

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