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A quasi-Newton type method for equilibrium problems

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Abstract

In this work, we develop a quasi-Newton-type method for equilibrium problems based on the proximal Newton-type structure given in Santos et al. (Optimization Letters 12(5), 997-1009, 2018). We consider a family of matrices verifying a bounded deterioration property. We prove that the sequence generated by the algorithm is well defined and under suitable assumptions we establish the linear convergence of the algorithm. Numerical experiments are reported.

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Funding

The third author was partially supported by CNPq Grant 311825/2019-2.

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Authors and Affiliations

  1. Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil

    Leonardo A. Sousa & Susana Scheimberg

  2. Universidade Federal do Delta do Parnaíba (UFDPar), Parnaíba, Brazil

    Pedro Jorge S. Santos & Paulo Sérgio M. Santos

Authors
  1. Leonardo A. Sousa
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  2. Susana Scheimberg
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  3. Pedro Jorge S. Santos
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  4. Paulo Sérgio M. Santos
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Correspondence to Pedro Jorge S. Santos.

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Sousa, L.A., Scheimberg, S., Santos, P.J.S. et al. A quasi-Newton type method for equilibrium problems. Numer Algor 89, 1129–1143 (2022). https://doi.org/10.1007/s11075-021-01148-z

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  • DOI: https://doi.org/10.1007/s11075-021-01148-z

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