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An Inexact Spingarn's Partial Inverse Method with Applications to Operator Splitting and Composite Optimization

Samara Costa Lima(samaraclim***at***outlook.com)
Maicon Marques Alves(maicon.alves***at***ufsc.br)

Abstract: We propose and study the iteration-complexity of an inexact version of the Spingarn's partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient (HPE) method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the iteration-complexity of an inexact operator splitting algorithm -- which generalizes the original Spingarn's splitting method -- and of a parallel forward-backward algorithm for multi-term composite convex optimization.

Keywords: Inexact proximal point methods, Partial inverse method, Splitting, Composite optimization, Forward-backward, Parallel, Iteration-complexity

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 10/29/2016
Entry Accepted: 10/29/2016
Entry Last Modified: 10/29/2016

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