中科院数学与系统科学研究院

科研进展与学术交流报告会

（第9期）

报告人一： 丁超 副研究员（应用数学研究所）

题 目 一：再探增广拉格朗日法

摘 要 一：自1969年由M.R. Hestenes和M.J.D. Powell提出以来，增广拉格朗日法以其深刻的优化理论以及求解优化问题时优异的数值效果，受到数学优化、机器学习等不同领域学者的广泛关注，并已被用于许多著名优化求解器以提高求解许多大规模约束优化问题的数值效果。在本讲座中，我们将结合矩阵优化最新理论结果，介绍增广拉格朗日法在求解非线性半正定优化、黎曼流形上的非光滑优化以及随机规划等问题的研究进展。最后，我们将简要介绍增广拉格朗日法在实际问题中的若干应用，特别是我们在诸如视频防抖处理、大规模集成电路设计等问题中的尝试以及面临的挑战。

报告人二： 高斌 副研究员（计算数学与科学工程计算研究所）

题 目 二：Optimization on matrix manifolds: a computational point of view

摘 要 二: Over the past few decades, optimization on manifolds has received increasing interest in research and engineering, recognized as a wide, beautiful and effective generalization of unconstrained optimization. These problems arise often in engineering applications, including in machine learning, computer vision, signal processing, dynamical systems and scientific computing. Involving a Riemannian structure on smooth manifolds is sufficient to define gradients and Hessians on the manifold, paving the way for optimization. Hence, we can generalize the standard algorithms from unconstrained optimization to handle the broader class of optimization over smooth manifolds. My talk is concerned with some specific manifolds including the Stiefel manifold, the symplectic Stiefel manifold, and fixed-rank manifolds. The purpose of my talk is to develop efficient algorithms for solving optimization problems on these manifolds and to study the Riemannian structure of manifolds.

时  间：2022.10.21(星期五), 10:40-13:00

地  点：数学院南楼N204室 / 腾讯会议141-527-587

报告会视频