On Inexact Relative-Error Hybrid Proximal Extragradient, Forward-Backward and Tseng’s Modified Forward-Backward Methods with Inertial Effects

  • M. Marques AlvesEmail author
  • Raul T. Marcavillaca


For solving monotone inclusion problems, we propose an inertial under-relaxed version of the relative-error hybrid proximal extragradient method. We study the asymptotic convergence of the method, as well as its nonasymptotic global convergence rates in terms of iteration complexity. We analyze the new method under more flexible assumptions than existing ones, both on the extrapolation and on the relative-error parameters. The approach is applied to two types of forward-backward type methods for solving structured monotone inclusions.


Inertial Relaxed Proximal point method HPE method Pointwise Ergodic Iteration-complexity Forward-backward algorithm Tseng’s modified forward-backward algorithm 

Mathematics Subject Classification (2010)

90C25 90C30 47H05 


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We are thankful to the two anonymous referees for their constructive suggestions which have improved the first version of this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Santa CatarinaFlorianópolisBrazil

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