报告题目：Error bounds for Structured Convex Programming: Theory and Applications

摘要：

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in practical implementation and convergence analysis of a host of iterative methods for solving optimization problems. In this talk, we present a new framework for establishing error bounds for a class of structured convex optimization problems, in which the objective function is the sum of a smooth convex function and a possibly nonsmooth convex function.  Such a class encapsulates not only fairly general constrained minimization problems but also various regularized loss minimization formulations in machine learning, signal processing, and statistics. Using our framework, we show that a number of existing error bound results can be recovered in a unified and transparent manner. To further demonstrate the power of our framework, we apply it to establish new error bounds for nuclear-norm and $/ell_{1,p}$-norm regularized loss minimization formulations. 

A Short Bio:

Dr. Zirui Zhou is currently an Alan Mekler Postdoctoral Fellow in the Department of Mathematics at Simon Fraser University. He received his Ph.D. in the Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong. Prior to that, he obtained his B.S. in the School for Gifted Young at University of Science and Technology of China. Dr. Zhou’s research area is mainly in continuous optimization and its application to machine learning, signal processing, and data analysis. His research works have been published in Mathematical Programming, Optimization Methods & Software, ICML, and NIPS.