Linearized Alternating Direction Method for Constrained Linear Least-squares Problem

In this paper, we apply the alternating direction method (ADM) to solve a constrained linear least-squares problem where the objective function is a sum of two least-squares terms and the constraints are box constraints. Using ADM, we decompose the original problem into two easier least-squares subproblems at each iteration. To speed up the inner iteration, we linearize the subproblems whenever their closed-form solutions do not exist. We prove the convergence of the resulting algorithm and apply it to solve some image deblurring problems. We show the efficiency of our algorithm by comparing it with Newton-type methods.