题  目: An iteratively reweigthed second-order method for nonconvex regularization

主讲人: 王浩 副教授

单  位: 上海科技大学

时  间: 3月16日10：30-12：30

地  点: 数学院106研讨室（线上：腾讯会议 424135280）

摘  要： This paper considers a class of nonconvex sparsity-promoting regularization problems with a twice continuously differentiable loss function. We present a second-order algorithm to solve this class of nonconvex and nonsmooth problems. Most existing algorithms are first-order methods, and a hybrid of the proximal gradient method and subspace regularized Newton method was proposed for $\ell_p$ regularization until recently. Our new method is also a hybrid method with main features including: (i) our method is based on the iteratively reweighted method with the regularization term being iteratively approximated by a weighted $\ell_1$ regularization term, so that it can be applied to various nonconvex regularization problems. (ii) Our method alternatively solves the $\ell_1$ approximation by a soft-thresholding step and the subspace approximate Newton step. (iii) The iterates generated by our algorithm have unchanged sign values, and the nonzero components are bounded away from 0 for sufficiently large iterations, and the algorithm eventually reverts to a perturbed Newton method. (iv) We prove global convergence and a local quadratic convergence rate under loose assumptions for our method and demonstrate its efficiency on a large set of model prediction problems.

简  介： 王浩博士，上海市青年东方学者。现任上海科技大学信息科学与技术学院副教授，于2015年5月在美国Lehigh大学工业工程系获得博士学位，并于2010年和2007年在北京航空航天大学数学与应用数学系分别获得理学硕士和学士学位。当前研究领域主要为非线性优化、非凸正则化问题等问题和算法。主要成果在SIAM Journal on Optimization，Journal of Machine Learning Research， IEEE on Computers等刊物上发表。