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, alternating direction method of multipliers, linearization, image processing.
AB - <p style="text-align: justify;">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.</p>