主讲人：王湘美

主办单位：数学与大数据学院

讲座时间：2021年4月15日上午9:00-10:00

讲座地点：知津楼C303

内容简介：

We study the convergence issue for the gradient algorithm (employing general step 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. linear convergence) results are established. As an application, the linear convergence properties of the gradient algorithm employing the constant step sizes and the Armijo step sizes for finding the Riemannian Lp (p 2 [1; +1)) centers of mass are explored, respectively, which in particular extend and/or improve the corresponding recent results in in [O. P. Ferreira, M. S. Louzeiro, and L. 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. 

讲座人简介：

贵州大学数学与统计学院副教授，硕士生导师，浙江大学理学博士，主要从事黎曼流形、巴拿赫空间上优化理论、优化算法研究及应用。发表SCI论文10余篇，其中优化理论的顶级刊物SIAM J Optim.2篇。主持国家自然科学基金一项，贵州省科技厅基金两项。