题目：            Riemannian Proximal Gradient Methods

报告人：       黄文 (厦门大学)

时间地点：   2019.09.26  16:00pm  N213

摘要：          We consider solving nonconvex and nonsmooth optimization problems with 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 gradient method and its variants have been viewed as excellent methods for solving nonconvex 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 Riemannian manifolds, in particular, the proximal gradient method on manifold. We develop and analyze a Riemannian proximal gradient method and its variant with 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/k^2) convergence rates are estiblished for the method and its variant under more assumptions. A pratical algorithm is also proposed. Two models in sparse PCA are used to demonstrate the performance of the proposed method. This is joint work with Ke Wei at Fudan University.