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Journal of Optimization Theory and Applications

, Volume 168, Issue 1, pp 198–215 | Cite as

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.

Keywords

Hybrid proximal extragradient method Strongly monotone operators Variational inequalities Tseng’s forward–backward method Korpelevich extragradient method 

Mathematics Subject Classification

47H05 47J20 90C060 90C33 65K10 

Notes

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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolisBrazil
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.IMPARio de JaneiroBrazil

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