Volume 2, Issue 4
Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem

Raymond H. Chan, Min Tao & Xiaoming Yuan

East Asian J. Appl. Math., 2 (2012), pp. 326-341.

Published online: 2018-02

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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

Linear least-squares problems alternating direction method linearization image processing

  • AMS Subject Headings

68U10 65J22 65K10 65T50 90C25

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-2-326, author = {Raymond H. Chan, Min Tao and Xiaoming Yuan}, title = {Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {4}, pages = {326--341}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.270812.161112a}, url = {http://global-sci.org/intro/article_detail/eajam/10880.html} }
TY - JOUR T1 - Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem AU - Raymond H. Chan, Min Tao & Xiaoming Yuan JO - East Asian Journal on Applied Mathematics VL - 4 SP - 326 EP - 341 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.270812.161112a UR - https://global-sci.org/intro/article_detail/eajam/10880.html KW - Linear least-squares problems KW - alternating direction method KW - linearization KW - image processing AB -

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.

Raymond H. Chan, Min Tao & Xiaoming Yuan. (1970). Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem. East Asian Journal on Applied Mathematics. 2 (4). 326-341. doi:10.4208/eajam.270812.161112a
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