报告人：孔令臣教授

报告题目：Newton method for the composite row sparsity regularized optimization

摘要：This paper is concerned with the composite row sparsity regularized (cRSR) minimization problem, which captures a number of important applications arising in machine learning, statistics, signal and image processing, and so forth. Due to the non-convexity and discontinuity of the composite row sparsity regularization term, the cRSR problem is NP-hard in general. In this paper, we study the optimality conditions of the cRSR problem and derive its stationary equation which is crucial to design efficient algorithm. Based on this stationary equation, an easy-to-implement Newton method is designed to solve the cRSR problem (NcRSR for short). The quadratic convergence rate and iteration complexity estimation of the NcRSR are rigorously proved under some mild conditions. To demonstrate the effectiveness of NcRSR, we apply it to solve the simultaneous clustering and optimization and trend filtering problems. Extensive experimental results illustrate that our approach has superior performance comparing to the state-of-the-art methods. In particular, NcRSR possesses not only perfect clustering performance and estimation accuracy but also one hundred times faster than the first-order methods.

报告时间：2022年6月29号下午14:00-16:30

报告形式：腾讯会议；会议号：664 4945 0076

报告人简介：孔令臣博士，北京交通大学数学与统计学院，教授，博士生导师，中国运筹学会数学规划分会副秘书长。2007年毕业于北京交通大学，获博士学位。2007-2009年，加拿大滑铁卢大学组合与优化系博士后。2009年9月入职北京交通大学数学系，2010年晋升为副教授，2014年晋升为教授。主要从事统计优化、高维统计分析、稀疏优化、对称锥互补和优化问题以及医学和交通应用等方面的研究。主持国家自然科学基金面上项目和参与973课题、国家自然科学基金重点项目以及北京市自然科学基金重点项目等，获得2012度中国运筹学会青年奖。