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An extragradient method for equilibrium problems on Hadamard manifolds

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Abstract

In this paper, we propose an extragradient algorithm for solving equilibrium problems on Hadamard manifolds to the case where the equilibrium bifunction is not necessarily pseudomonotone. Under mild assumptions, we establish global convergence results. We show that the multiobjective optimization problem satisfies all the hypotheses of our result of convergence, when formulated as an equilibrium problem.

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Acknowledgments

The authors are grateful to the editor and the referee for their valuable comments and suggestions. The first author was partially supported by CNPq Grant 305462/2014-8 and PRONEX-Optimization (FAPERJ/CNPq) and the second author was supported in part by CNPq Grant 485205/2013-0, with additional support from PROPESQ/UFPI. Part of this work was carried out while the authors were visiting the IMPA - Instituto Nacional de Matemática Pura e Aplicada.

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Authors and Affiliations

  1. DM/UFPI, Teresina, Brazil

    J. X. Cruz Neto

  2. CMRV/UFPI, Parnaíba, Brazil

    P. S. M. Santos

  3. DM/UESPI, Teresina, Brazil

    P. A. Soares Jr

Authors
  1. J. X. Cruz Neto
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  2. P. S. M. Santos
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  3. P. A. Soares Jr
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Correspondence to P. S. M. Santos.

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Cruz Neto, J.X., Santos, P.S.M. & Soares, P.A. An extragradient method for equilibrium problems on Hadamard manifolds. Optim Lett 10, 1327–1336 (2016). https://doi.org/10.1007/s11590-015-0933-0

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  • DOI: https://doi.org/10.1007/s11590-015-0933-0

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