流形优化系列短课程1：最优化方法基础
Riemannian Optimization Series 1: Basics on Optimization
课程简介
黎曼流形上的优化，也被称为黎曼优化或流形优化，考虑最小化定义在黎曼流形上的实值函数。如今信息时代的数据规模越来越大，许多问题中的高维数据会落在低维流形上，分析处理
这些数据往往会将其转换成为黎曼优化问题。这些领域包括但不限于信号处理，机器学习，推荐系统，网络成分分析与分类，计算机视觉与图形学等。这使得黎曼优化在这几年受到越
来越多的关注。
此课程为流形优化系列短课程第一期。本期课程通过介绍必要的欧式优化算法，为后续流形优化课程打基础。本课程围绕无约束光滑优化算法展开。主要内容包括无约束光滑优化的理论基础、
一阶线性搜索算法、二阶线性搜索算法及其理论结果。
Abstract
Optimization on Riemannian mainfolds, also called Riemannian optimization, considers finding an optimum of a real-valued function defined on a Riemannian manifold. Riemannian optimization has been a topic of much interest over the past few years due to many important applications, e.g., blind source separation, computations on symmetric positive matrices, low-rank learning, graph similarity, community detection, and elastic shape analysis.
This is the Series 1 of the Riemannian optimization short courses. In this short course, we focus on unconstrained smooth optimization basics and methods in Euclidean space, in order to lay foundation for later short courses. This course covers theoretical basics, first order line search based methods, second order line search based methods, and their convergence results.
课程信息 Course Information
- 教师信息：黄文 教授（厦门大学）
- 教师邮箱：wen.huang at xmu dot edu dot cn
- 课程学时：10学时
- 授课时间：11月2、4、5日，上午9:00-11:30
- 授课地点：线上授课
课程资料 Course Materials