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A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis

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Abstract

This paper presents and studies the iteration-complexity of a variant of the hybrid proximal extragradient method for solving inclusion problems with strongly (maximal) monotone operators. As applications, we propose and analyze two special cases: variants of the Tseng’s forward–backward method for solving monotone inclusions with strongly monotone and Lipschitz continuous operators and of the Korpelevich extragradient method for solving (strongly monotone) variational inequalities.

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Acknowledgments

M. Marques Alves was partially supported by CNPq Grant Nos. 406250/2013-8, 237068/2013-3 and 306317/2014-1. B. F. Svaiter was partially supported by CNPq Grant Nos. 474996/2013-1, 302962/2011-5 and FAPERJ Grant E-26/201.584/2014.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brazil

    Maicon Marques Alves

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    Maicon Marques Alves

  3. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil

    B. F. Svaiter

Authors
  1. Maicon Marques Alves
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  2. B. F. Svaiter
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Correspondence to Maicon Marques Alves.

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Marques Alves, M., Svaiter, B.F. A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis. J Optim Theory Appl 168, 198–215 (2016). https://doi.org/10.1007/s10957-015-0792-y

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  • DOI: https://doi.org/10.1007/s10957-015-0792-y

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