Convergence rate of a proximal multiplier algorithm for separable convex minimization

Orlando Sarmiento (osarmientocos.ufrj.br)
Erik Papa Quiroz (erikpapagmail.com)
Paulo Oliveira (oliveira.paulorobertogmail.com)

Abstract: The proximal multiplier method with proximal distances (PMAPD) proposed by O. Sarmiento C., E. A. Papa Quiroz and P. R. Oliveira, applied to solve a convex program with separable structure unified the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM) and extended the convergence properties for the class of $\varphi-$divergence distances. In this paper, we show that under standard assumptions the iterations generated by the (PMAPD) converge linearly to the unique optimal solution of the problem.

Keywords: Proximal multiplier method; separable convex problem; proximal distances

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Report2-PRO, PESC-COPPE-UFRJ

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Entry Submitted: 03/13/2015
Entry Accepted: 03/13/2015
Entry Last Modified: 06/24/2015

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