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

Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem
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Year:    2012

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.270812.161112a

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 326–341

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Linear least-squares problems alternating direction method of multipliers linearization image processing.

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