Linearized alternating direction method for constrained linear least-squares problem
Speaker:Prof. Raymond H. Chan
Chair Professor
The Chinese University of Hong Kong
Date & Time:10 Apr 2013 (Wednesday) 14:00
Venue:J419
Organized by:Department of Mathematics

Abstract

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 where the matrices involved are structured matrices. We show the efficiency of our algorithm by comparing it with Newton-type methods. Extension to TV-type problems will also be discussed.

Biography

Prof. Raymond Chan is a Choh-Ming Li Chair Professor and the Chairman of the Department of Mathematics at The Chinese University of Hong Kong . Prof. Chan has published 110 journal papers and has been in the ISI Science Citation List of Top 250 Highly-Cited Mathematicians in the world since 2004. He won a Leslie Fox Prize for Numerical Analysis in 1989 at Cambridge in the United Kingdom; a Feng Kang Prize in 1997 in Beijing, China; a Morningside Award in 1998 in Beijing, China; and 2011 Higher Education Outstanding Scientific Research Output Awards (First Prize) from the Ministry of Education in China. He was elected SIAM fellow in 2013.