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Hybrid proximal methods for equilibrium problems

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Abstract

This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Boris S. Mordukhovich

  2. Department of Applied Mathematics, University of Pisa, via Buonarroti 1/c, 56127, Pisa, Italy

    Barbara Panicucci, Massimo Pappalardo & Mauro Passacantando

Authors
  1. Boris S. Mordukhovich
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  2. Barbara Panicucci
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  3. Massimo Pappalardo
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  4. Mauro Passacantando
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Corresponding author

Correspondence to Mauro Passacantando.

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Mordukhovich, B.S., Panicucci, B., Pappalardo, M. et al. Hybrid proximal methods for equilibrium problems. Optim Lett 6, 1535–1550 (2012). https://doi.org/10.1007/s11590-011-0348-5

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  • DOI: https://doi.org/10.1007/s11590-011-0348-5

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