报告题目 (Title)：A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian submanifolds in Euclidean space（求解欧式空间黎曼子流形上非光滑优化的流行非精确增广拉格朗日方法）

报告人 (Speaker)：彭拯 博士 (湘潭大学)

报告时间：2023年8月2日（周三）10:00

参会方式：校本部F309

邀请人：周安娃

主办部门：理学院数学系

报告摘要：We develop a manifold inexact augmented Lagrangian framework to solve a family of nonsmooth optimization problem on Riemannian submanifold embedding in Euclidean space, whose objective function is the sum of a smooth function (but possibly nonconvex) and a nonsmooth convex function in Euclidean space. By utilizing the Moreau envelope, we get a smoothing Riemannian minimization subproblem at each iteration of the proposed method. Consequentially, each iteration subproblem is solved by a Riemannian Barzilai-Borwein gradient method. Theoretically, the convergence to critical point of the proposed method is established under some mild assumptions. Numerical experiments on compressed modes problems in Physic and sparse principal component analysis demonstrate that, the proposed method is a competitive method compared to some state-of-the-art methods.