11月3日 Xiaojun Chen教授学术报告

发布时间:2014-10-24

题 目：Nonconvex Regularized Optimization for Sparse Approximations

报告人：Xiaojun Chen, Chair Professor of Applied Mathematics
(Department of Applied Mathematics, The Hong Kong Polytechnic University)

时 间： 11月3日（周一） 下午3:00-4:00

地 点： 旧数学楼104室

Abstract:
Minimization problems with nonsmooth, nonconvex, perhaps even non-Lipschitz regularization terms have wide applications in image restoration, signal reconstruction and variable selection. On $L_p$ non-Lipschitz regularized minimization, 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 without assumptions on the data matrix. 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 reweighted $L_1$ minimization algorithms, smoothing quadratic regularization algorithms, smoothing trust region Newton methods and interior point algorithms. Examples with six widely used nonsmooth nonconvex regularization terms are presented to illustrate the theory and algorithms.

个人简介：
http://www.polyu.edu.hk/ama/staff/xjchen/ChenXJ.htm

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