A customized proximal point algorithm for convex minimization with linear constraints

Bingsheng He; Xiaoming Yuan; Wenxing Zhang

doi:10.1007/s10589-013-9564-5

A customized proximal point algorithm for convex minimization with linear constraints

Bingsheng He, Xiaoming Yuan^*, Wenxing Zhang

^*Corresponding author for this work

Department of Mathematics

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

47 Citations (Scopus)

Abstract

This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.

Original language	English
Pages (from-to)	559-572
Number of pages	14
Journal	Computational Optimization and Applications
Volume	56
Issue number	3
DOIs	https://doi.org/10.1007/s10589-013-9564-5
Publication status	Published - Dec 2013

Scopus Subject Areas

Control and Optimization
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Augmented Lagrangian method
Convex minimization
Proximal point algorithm
Resolvent operator

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10.1007/s10589-013-9564-5

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abstract = "This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.",

keywords = "Augmented Lagrangian method, Convex minimization, Proximal point algorithm, Resolvent operator",

author = "Bingsheng He and Xiaoming Yuan and Wenxing Zhang",

note = "Funding Information: B. He was supported by the NSFC grant 91130007 and the grant of MOE of China 20110091110004. Funding Information: X. Yuan was supported by the General Research Fund from Hong Kong Research Grants Council: 203712.",

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AU - Yuan, Xiaoming

AU - Zhang, Wenxing

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PY - 2013/12

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N2 - This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.

AB - This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.

KW - Augmented Lagrangian method

KW - Convex minimization

KW - Proximal point algorithm

KW - Resolvent operator

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JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 3

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A customized proximal point algorithm for convex minimization with linear constraints

Abstract

Scopus Subject Areas

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