Error bounds for Structured Optimization Problems: Theory and Applications
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：周子锐
：2019-11-19 16:30
：实验楼108
Speaker：Dr. Zirui Zhou
Hong Kong Baptist University
Title: Error bounds for Structured Optimization Problems: Theory Applications
Time：19 Nov 2019, 16:30
Location：实验楼108
Abstract: 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 convergence analysis of a host of iterative methods for solving optimization problems. In the first part of this talk, we shall present a framework for verifying the validity of error bounds for a class of structured convex optimization problems, which encapsulates not only fairly general constrained minimization problems but also various regularized loss minimization formulations in machine learning, signal processing, statistics. Using our framework, we show that a number of existing error bound results can be recovered in a unified transparent manner. To further demonstrate the power of our framework, we apply it to establish new error bounds for nuclear-norm $\ell_{1,p}$-norm regularized loss minimization formulations. We shall also show how these error bounds can be exploited to develop efficient second-order methods for solving such class of problems. In the second part of this talk, we shall consider a class of smooth nonconvex optimization formulations that are recently becoming popular for tackling problems like low-rank matrix recovery phase retrieval. We show that this class of nonconvex problems also possesses favorable error bounds, which can be exploited to establish quadratic convergence of the cubic regularization method for solving such class of problems.
Speaker Introduction：周子锐，香港浸会大学数学系助理教授，2015年于香港中文大学获得系统工程与工程管理博士学位。2016至2018年度，在西蒙弗雷泽大学数学和统计系从事博士后研究。他的主要研究方向为连续优化的理论和算法，及其在机器学习和信号处理等领域的应用。至今已在SIAM Journal on Optimization和Mathmetical Programming等优化国际顶级期刊上发表数篇论文。
联系人：黄文副教授
