报告题目1：Theory and algorithms for two-stage stochastic variational inequalities

报告时间：1月25日14：40 – 15：40

报告地点：数学与统计学院会议室（414-2）

报 告 人：陈小君教授

报告摘要：The two-stage stochastic variational inequality (SVI) provides a powerful modeling paradigm for many important applications in which uncertainties and equilibrium are present. The two-stage SVI is to find a pair: here-and-now solution and wait-and-see solution. The here-and-now solution represents now-decisions, while the wait-and-see solution depends on future events described by random variables. This talk reviews new developments in theory and algorithms for two-stage stochastic variational inequalities.

报告题目2：Nonsmooth, Nonconvex Regularization for Sparse Portfolio Selection

报告时间：1月25日16：00 – 17：00

报告地点：数学与统计学院会议室（414-2）

报 告 人：陈小君教授

报告摘要：We consider a class of constrained minimization problems where the objective function is a sum of a smooth function and a nonsmooth, nonconvex, perhaps even non-Lipschitz regularization. On concave regularization including SCAD, MCP and $L_p$ norm ($0<p<1$), we show that finding a global optimal solution is strongly 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 and select regularization parameters for desirable sparsity of 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 and image restoration are presented to illustrate the theory and algorithms.

报告人简介：陈小君，香港理工大学应用数学系讲座教授，系主任，博士生导师。主要研究领域：变分不等式、均衡问题、互补问题及其应用；非光滑优化；随机优化与并行算法等。陈小君教授主持香港研究基金项目11项，日本科学促进会项目5项，澳大利亚研究理事会项目3项等众多科研课题。她是《SIAM Journal on Numerical Analysis》、《Numerical Functional Analysis and Optimization》、《Numerical Algorithms》《Journal of Industrial and Management Optimization》、《Science China Mathematics》等国际十余种著名刊物的编委，至今已在国际著名刊物上发表学术论文一百余篇，包括《Mathematical Programming》、《SIAM J. Optimization》、《SIAM J. Numerical Analysis》、《Numerische Mathematik》、《SIAM J. Scientific Computing》、《SIAM J. Matrix Anal. Applications》等国际顶尖学术期刊。她是美国数学评论评论员、美国工业与应用学会会员、国际数学规划协会会员，曾多次在国际学术会议上做邀请报告，如曾于2012年在国际数学规划会议上作特邀报告。