报告题目：Nonsmooth, Nonconvex Regularization for Sparse Portfolio Selection

报告摘要：We consider a class of constrained minimization problems where the objective functions is a sum of a smooth function and a nonsmooth, nonconvex, perhaps even non-Lipschitz regularization. On concave regularization including SCAD, MCP and norm(0<p<1), we show that funding a global optimal solution is strong NP-hard. On the other hand, we present lower bounds of nonzero entries in every local optimal solution. Such lower bounds can be used to classify zero and nonzero entries in local optimal solutions. Moreover, we introduce several efficient algorithms including smoothing quadratic regularization algorithms, smoothing trust region Newton methods, interior point algorithms and augmented Lagrangian methods. Examples of sparse portfolio selection are presented to illustrate the theory and algorithms.  

报告时间：2017年4月14日（周五）下午15：00-16：00

报告地点：长清湖校区B区4楼伟德国际1946源自英国报告厅

欢迎老师和同学参加！

报告人简介：陈小君，香港理工大学数学系讲座教授，应用数学系主任。主要研究领域：关于非线性或奇异或非光滑方程组的迭代算法；补偿问题及其应用；非光滑优化；随机优化与平行算法等。主持香港RGC项目9项，主持日本JSPS项目5项，主持澳大利亚ARC项目3项等。已在国际著名刊物如：Math. Programming，SIAM J. Optimization，SIAM J. Numerical Analysis等上发表一百多篇学术论文，曾于2012年在国际数学规划会议上作大会特邀报告。