Riemannian Proximal Gradient Methods
报告人:黄文 副教授, 厦门大学数学科学学院 时间:2019年10月24日16:30
邀请人: 姜波 副教授
摘要:We consider solving nonconvex and nonsmooth optimization problemswith Riemannian manifold constraints. Such problems have received considerable attention due to many important applications such as sparse PCA,sparse blind deconvolution, robust matrix completion. Many of the applications yield composite objectives. In the Euclidean setting, proximal gradientmethod and its variants have been viewed as excellent methods for solvingnonconvex nonsmooth problems with composite cost functions. However,in the Riemannian setting, the related work is still limited. In this talk,we briefly review exisitng non-smooth optimization methods on Riemannianmanifolds, in particular, the proximal gradient method on manifold. We develop and analyze a Riemannian proximal gradient method and its variantwith acceleration. It is shown that the global convergence is obtained for the
Riemannian proximal gradient method under mild assumptions. The O(1=k)and O(1=k2) convergence rates are estiblished for the method and its variantunder more assumptions. A pratical algorithm is also proposed. Two models in sparse PCA are used to demonstrate the performance of the proposedmethod.This is joint work with Ke Wei at Fudan University.