摘 要：

In this talk, we consider the convergence behavior of the alternating direction method of multipliers (ADMM) for solving regularized non-convex low-rank matrix recovery problems. We show that the ADMM will converge globally to a critical point of the problem without making any assumption on the sequence generated by the method. Furthermore, if the objective function of the problem satisfies the Lojasiewicz inequality with exponent 1/2 at every (globally) optimal solution, then with suitable initialization, the ADMM will converge linearly to an optimal solution. We then complement this result by showing that three popular formulations of the low-rank matrix recovery problem satisfy the aforementioned Lojasiewicz inequality, which may be of independent interest. Consequently, we are able to exhibit, for the first time, concrete instances of non-convex optimization problems for which the ADMM converges linearly. As a by-product, we establish the global convergence and local linear convergence of the block coordinate descent (BCD) method for solving regularized non-convex matrix factorization problems.

报告人简介:

Anthony Man-Cho So joined The Chinese University of Hong Kong (CUHK) in 2007, where he currently serves as Associate Dean of Student Affairs in the Faculty of Engineering and is Professor in the Department of Systems Engineering and Engineering Management. His recent research focuses on the interplay between optimization theory and various areas of algorithm design, such as computational geometry, machine learning, signal processing, and algorithmic game theory.

 Dr. So is a member of the editorial boards of Journal of Global Optimization, Optimization Methods and Software, and SIAM Journal on Optimization. He has received a number of research and teaching awards, including the 2018 IEEE Signal Processing Society Best Paper Award, the 2015 IEEE Signal Processing Society Signal Processing Magazine Best Paper Award, the 2014 IEEE Communications Society Asia-Pacific Outstanding Paper Award, and the 2010 Institute for Operations Research and the Management Sciences (INFORMS) Optimization Society Optimization Prize for Young Researchers, as well as the 2013 CUHK Vice-Chancellor's Exemplary Teaching Award, the 2011, 2013, 2015 CUHK Faculty of Engineering Dean's Exemplary Teaching Award, and the 2008 CUHK Faculty of Engineering Exemplary Teaching Award. He also co-authored with his student a paper that receives the Best Student Paper Award at the 19th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2018).

报告人：苏文藻

地点：计算机科学技术楼230室