A proximal multiplier method for separable convex minimization

O. Sarmiento; E. A. Papa Quiroz; P. R. Oliveira

doi:10.1080/02331934.2015.1062009

A proximal multiplier method for separable convex minimization

O. Sarmiento, E. A. Papa Quiroz, P. R. Oliveira

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper, we propose an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure. The proposed method unifies the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM), and extends the convergence properties for the class of (Formula presented.) -divergence distances. We prove, under standard assumptions, that the iterations generated by the method are well defined and the sequence converges to an optimal solution of the problem.

Original language	English
Pages (from-to)	501-537
Number of pages	37
Journal	Optimization
Volume	65
Issue number	2
DOIs	https://doi.org/10.1080/02331934.2015.1062009
State	Published - 1 Feb 2016

Bibliographical note

Funding Information:
The research of the first and second authors was supported by CAPES (Coordenaçço de Aperfeiçoamento de Pessoal de Nível Superior) and the PosDoctoral Scolarchip CAPES-FAPERJ Edital PAPD-2011, respectively.

Publisher Copyright:
© 2015 Taylor & Francis.

Keywords

convex functions
proximal distances
proximal multiplier methods
separable convex problems

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10.1080/02331934.2015.1062009

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AU - Papa Quiroz, E. A.

AU - Oliveira, P. R.

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N2 - In this paper, we propose an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure. The proposed method unifies the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM), and extends the convergence properties for the class of (Formula presented.) -divergence distances. We prove, under standard assumptions, that the iterations generated by the method are well defined and the sequence converges to an optimal solution of the problem.

AB - In this paper, we propose an inexact proximal multiplier method using proximal distances for solving convex minimization problems with a separable structure. The proposed method unifies the works of Chen and Teboulle (PCPM method), Kyono and Fukushima (NPCPMM) and Auslender and Teboulle (EPDM), and extends the convergence properties for the class of (Formula presented.) -divergence distances. We prove, under standard assumptions, that the iterations generated by the method are well defined and the sequence converges to an optimal solution of the problem.

KW - convex functions

KW - proximal distances

KW - proximal multiplier methods

KW - separable convex problems

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M3 - Artículo

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VL - 65

SP - 501

EP - 537

JO - Optimization

JF - Optimization

IS - 2

ER -

A proximal multiplier method for separable convex minimization

Abstract

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Keywords

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