报告题目：A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold

报告人：彭拯

报告时间：2022年9月16日09:00-11:30

报告地点：腾讯会议：372-367-038

邀请单位：福州大学数学与统计学院，离散数学及其应用省部共建教育部重点实验室

报告内容简介：Abstract：In this talk, we consider a nonsmooth optimization problem on Riemannian manifold, whose objective function is the sum of a differentiable component and a nonsmooth convex function. We first reformulate this problem to a separable form, and then propose a manifold inexact augmented Lagrangian method for the resulting problem. By utilizing the Moreau envelope, we get a smoothing subproblem at each iteration of the proposed method. Theoretically, the convergence to critical point of the proposed method is established under some mild assumptions. In particular, if an approximate global minimizer of the iteration subproblem is obtained at each iteration, we prove that the sequence generated by the proposed method converges to a global minimizer of the origin problem. Numerical experiments show that, the proposed method is a competitive method compared to some existing methods.

Keywords: Manifold optimization; Nonsmooth optimization; Augmented Lagrangian method; Moreau envelope.

报告人简介：

彭拯，湘潭大学数学与计算科学学院教授，博士生导师，当前主要研究兴趣数据科学中的流形优化问题算法及其应用、卫星遥感数据融合、芯片设计与仿真等领域的工程优化问题及其高效率算法。彭拯教授2008年获上海大学博士学位，2010年从南京大学数学系博士后出站, 2013年晋升教授，在数学优化及其应用相关主流期刊发表学术论文40多篇，其中SCI、EI检索30余篇，完成国家、省部级科研项目10余项，当前主持在研国家自然科学基金面上项目和湖南省自然科学基金面上项目各1项。