A splitting method for separable convex programming

Bingsheng He; Min Tao; Xiaoming YUAN

doi:10.1093/imanum/drt060

A splitting method for separable convex programming

Bingsheng He, Min Tao, Xiaoming YUAN^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

62 Citations (Scopus)

Abstract

We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m individual functions without coupled variables. Treating the functions in the objective separately, the new method belongs to the category of operator splitting methods. We show the global convergence and estimate a worst-case convergence rate for the new method, and then illustrate its numerical efficiency by some applications.

Original language	English
Pages (from-to)	394-426
Number of pages	33
Journal	IMA Journal of Numerical Analysis
Volume	35
Issue number	1
DOIs	https://doi.org/10.1093/imanum/drt060
Publication status	Published - 21 Jun 2013

Scopus Subject Areas

Mathematics(all)
Computational Mathematics
Applied Mathematics

User-Defined Keywords

convex programming
image processing
operator splitting methods
separable structure

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10.1093/imanum/drt060

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keywords = "convex programming, image processing, operator splitting methods, separable structure",

author = "Bingsheng He and Min Tao and Xiaoming YUAN",

note = "Funding Information: B.H. was supported by the NSFC grants 10971095 and 91130007, and the MOEC fund 20110091110004. X.Y. was supported by the Hong Kong General Research Fund: HKBU 203311.",

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AU - Tao, Min

AU - YUAN, Xiaoming

N1 - Funding Information: B.H. was supported by the NSFC grants 10971095 and 91130007, and the MOEC fund 20110091110004. X.Y. was supported by the Hong Kong General Research Fund: HKBU 203311.

PY - 2013/6/21

Y1 - 2013/6/21

N2 - We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m individual functions without coupled variables. Treating the functions in the objective separately, the new method belongs to the category of operator splitting methods. We show the global convergence and estimate a worst-case convergence rate for the new method, and then illustrate its numerical efficiency by some applications.

AB - We propose a splitting method for solving a separable convex minimization problem with linear constraints, where the objective function is expressed as the sum of m individual functions without coupled variables. Treating the functions in the objective separately, the new method belongs to the category of operator splitting methods. We show the global convergence and estimate a worst-case convergence rate for the new method, and then illustrate its numerical efficiency by some applications.

KW - convex programming

KW - image processing

KW - operator splitting methods

KW - separable structure

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M3 - Journal article

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EP - 426

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JF - IMA Journal of Numerical Analysis

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A splitting method for separable convex programming

Abstract

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