报告题目: On the Quadratic Convergence of the Cubic Regularization Method under a Local Error Bound Condition
报告人：苏文藻教授，香港中文大学
报告时间： 2018年10月18日10:30－ 11:30
报告地点：行健楼学术活动室526
邀请人：姜波副教授
摘要: We revisit the cubic regularization (CR) method for solving smooth non-convex optimization problems and study its local convergence behavior. We show that under a local error bound (EB) condition, the sequence of iterates of the CR method converges quadratically to a local minimum. Moreover, we establish the equivalence between our EB condition and a quadratic growth condition. Using this equivalence, we prove that our EB condition holds if the function is gradient dominated or star-convex and globally non-degenerate. Consequently, the CR method converges quadratically when applied to these functions, thus improving the superlinear convergence results of Nesterov and Polyak. Finally, we apply our results to two concrete non-convex optimization problems that arise from phase retrieval and low-rank matrix recovery. For both problems, we prove that with overwhelming probability, the local EB condition is satisfied and the CR method converges quadratically to a global optimizer.
报告人简介：Anthony Man-Cho So joined the Chinese University of Hong Kong (CUHK) in 2007. 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 currently serves on the editorial boards of Journal of Global Optimization, Optimization Methods and Software, and SIAM Journal on Optimization. Dr. So has received a number of research and teaching awards, including the 2015 IEEE Signal Processing Society Signal Processing Magazine Best Paper Award, the 2014 IEEE Communications Society Asia-Pacific Outstanding Paper Award, the 2010 Institute for Operations Research and the Management Sciences (INFORMS) Optimization Society Optimization Prize for Young Researchers, and the 2013 CUHK Vice-Chancellor's 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).