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An augmented Lagrangian based parallel splitting method for separable convex minimization with applications to image processing


Authors: Deren Han, Xiaoming Yuan and Wenxing Zhang
Journal: Math. Comp. 83 (2014), 2263-2291
MSC (2010): Primary 90C06, 90C25, 94A08
DOI: https://doi.org/10.1090/S0025-5718-2014-02829-9
Published electronically: April 1, 2014
MathSciNet review: 3223332
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Abstract: This paper considers the convex minimization problem with linear constraints and a separable objective function which is the sum of many individual functions without coupled variables. An algorithm is developed by splitting the augmented Lagrangian function in a parallel way. The new algorithm differs substantially from existing splitting methods in alternating style which require solving the decomposed subproblems sequentially, while it remains the main superiority of existing splitting methods in that the resulting subproblems could be simple enough to have closed-form solutions for such an application whose functions in the objective are simple. We show applicability and encouraging efficiency of the new algorithm by some applications in image processing.


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Additional Information

Deren Han
Affiliation: School of Mathematical Science, Nanjing Normal University, Nanjing 210023, People’s Republic of China
Email: handeren@njnu.edu.cn

Xiaoming Yuan
Affiliation: Corresponding author. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong, People’s Republic of China
Email: xmyuan@hkbu.edu.hk

Wenxing Zhang
Affiliation: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
Email: wenxing84@gmail.com

DOI: https://doi.org/10.1090/S0025-5718-2014-02829-9
Keywords: Augmented Lagrangian method, convex programming, splitting method, parallel, image processing.
Received by editor(s): February 16, 2012
Received by editor(s) in revised form: December 1, 2012
Published electronically: April 1, 2014
Additional Notes: The first author was supported by NSFC Grants 11071122, 11171159, and 20103207110002 from MOE of China.
The second author was supported by the General Research Fund from Hong Kong Research Grants Council: HKBU203311.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.