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Regularized HPE-type methods for solving monotone inclusions with improved pointwise iteration-complexity bounds

Maicon Marques Alves(maicon.alves***at***ufsc.br)
Renato D.C. Monteiro(renato.monteiro***at***isye.gatech.edu)
Benar F. Svaiter(benar***at***impa.br)

Abstract: This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the HPE method while approaches (up to a logarithmic factor) the ergodic iteration-complexity of the latter method.

Keywords: proximal point methods, hybrid proximal extragradient method, pointwise iterationcomplexity, ergodic iteration-complexity, Tseng’s MFBS method, Korpelevich’s extragradient method.

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 09/08/2015
Entry Accepted: 09/08/2015
Entry Last Modified: 09/08/2015

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