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Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem

Published online by Cambridge University Press:  28 May 2015

Raymond H. Chan ,
Min Tao  and
Xiaoming Yuan
Raymond H. Chan*
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, China
Min Tao*
Affiliation:
School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, China
Xiaoming Yuan*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
*
Corresponding author. Email: rchan@math.cuhk.edu.hk
Corresponding author. Email: taom@njupt.edu.cn
Corresponding author. Email: xmyuan@hkbu.edu.hk
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Abstract.

The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no known closed-form solution. We prove the convergence of the resulting algorithm, and apply it to solve some image deblurring problems. Its efficiency is demonstrated, in comparison with Newton-type methods.

Keywords

68U1065J2265K1065T5090C25Linear least-squares problemsalternating direction method of multiplierslinearizationimage processing
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 4 , November 2012 , pp. 326 - 341
Copyright
Copyright © Global-Science Press 2012

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