讲座名称：Convergence Analysis of Gradient Algorithms on Riemannian Manifolds with Applications to Riemannian Mass

主讲人：李冲

时间：2021年6月24日14: 30  

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报告摘要

We study the convergence issue for the gradient algorithm (employing generalstep sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasiconvexity (resp. weak sharp minima), local/global convergence (resp. Linearconvergence) results are established. As an application, the linear convergence properties of the gradient algorithm employing the constant step sizesand the Armijo step sizes for finding the Riemannian Lp (p ∈ [1, +∞)) centersof mass are explored, respectively, which in particular extend and/or improvethe corresponding recent results in in [O. P. Ferreira, M. S. Louzeiro, andL. F. Prudente, SIAM J. Optim., 29 (2019), pp. 2517–2541, B. Afsari, R.Tron, and R. Vidal, SIAM J. Control Optim., 51 (2013), pp. 2230–2260; G.C. Bento et al., J. Optim. Theory Appl., 183 (2019), pp. 977–992], etc.  

This work is joint work with Professors Jinhua Wang (Hangzhou normal University), Xiangmei Wang (Guizhou University) and J.-C. Yao (ChinaMedical University, Taiwan).  

专家简介

李冲，浙江大学数学系教授，博士生导师。主要从事非线性优化理论与计算、数值泛函分析、数值代数、稀疏优化及其应用、机器学习等领域的研究。先后主持国家自然科学基金及省部级项目等近二十项，出版专著1部，在SCI期刊上发表论文近200篇， 特别是在优化理论和计算数学的顶级刊物SIAM J Optim., Math. Program，SIAM J. Control Optim.以及SIAM J.Numer. Anal上发表论文近30篇。1992年起享受国务院政府特殊津贴，获浙江省教委科技进步奖一、二等奖等奖励，原商业部有突出贡献的中青年专家、江苏省第七届青年科学家等，2004年获教育部首届新世纪优秀人才计划资助。