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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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  • Maicon Marques Alves

    (Universidade Federal de Santa Catarina
    Georgia Institute of Technology)

  • B. F. Svaiter

    (IMPA)

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.

Suggested Citation

  • Maicon Marques Alves & B. F. Svaiter, 2016. "A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 198-215, January.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0792-y
    DOI: 10.1007/s10957-015-0792-y
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    References listed on IDEAS

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    1. Renato Monteiro & Camilo Ortiz & Benar Svaiter, 2014. "Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems," Computational Optimization and Applications, Springer, vol. 57(1), pages 45-69, January.
    2. NESTEROV, Yurii & SCRIMALI, Laura, 2011. "Solving strongly monotone variational and quasi-variational inequalities," LIDAM Reprints CORE 2357, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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