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
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Taylor & Francis.

Keywords

convex functions
proximal distances
proximal multiplier methods
separable convex problems

Access to Document

10.1080/02331934.2015.1062009

Cite this

@article{1bde59f38e9641599baaa4750280335f,

title = "A proximal multiplier method for separable convex minimization",

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.",

keywords = "convex functions, proximal distances, proximal multiplier methods, separable convex problems",

author = "O. Sarmiento and {Papa Quiroz}, {E. A.} and Oliveira, {P. R.}",

note = "Publisher Copyright: {\textcopyright} 2015 Taylor & Francis.",

year = "2016",

month = feb,

day = "1",

doi = "10.1080/02331934.2015.1062009",

language = "Ingl{\'e}s",

volume = "65",

pages = "501--537",

journal = "Optimization",

issn = "0233-1934",

publisher = "Taylor and Francis Ltd.",

number = "2",

}

TY - JOUR

T1 - A proximal multiplier method for separable convex minimization

AU - Sarmiento, O.

AU - Papa Quiroz, E. A.

AU - Oliveira, P. R.

PY - 2016/2/1

Y1 - 2016/2/1

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

UR - http://www.scopus.com/inward/record.url?scp=84953364857&partnerID=8YFLogxK

U2 - 10.1080/02331934.2015.1062009

DO - 10.1080/02331934.2015.1062009

M3 - Artículo

AN - SCOPUS:84953364857

SN - 0233-1934

VL - 65

SP - 501

EP - 537

JO - Optimization

JF - Optimization

IS - 2

ER -

A proximal multiplier method for separable convex minimization

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this