TY - JOUR T1 - Linearized Alternating Direction Method of Multipliers for Constrained Linear Least-Squares Problem 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, alternating direction method of multipliers, linearization, 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.