A Brief Introduction to Manifold Optimization  

作　　者：Jiang Hu Xin Liu Zai-Wen Wen Ya-Xiang Yuan 

机构地区：[1]Beijing International Center for Mathematical Research,Peking University,Beijing 100871,China [2]State Key Laboratory of Scientific and Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]University of Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Journal of the Operations Research Society of China》2020年第2期199-248,共50页中国运筹学会会刊（英文）

基　　金：Xin Liu’s research was supported in part by the National Natural Science Foundation of China(No.11971466);Key Research Program of Frontier Sciences,Chinese Academy of Sciences(No.ZDBS-LY-7022);the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences and the Youth Innovation Promotion Association,CAS.Zai-Wen Wen’s research was supported in part by the the National Natural Science Foundation of China(Nos.11421101 and 11831002);the Beijing Academy of Artificial Intelligence.Ya-Xiang Yuan’s research was supported in part by the National Natural Science Foundation of China(Nos.11331012 and 11461161005).

摘　　要：Manifold optimization is ubiquitous in computational and appliedmathematics,statistics,engineering,machine learning,physics,chemistry,etc.One of the main challenges usually is the non-convexity of the manifold constraints.By utilizing the geometry of manifold,a large class of constrained optimization problems can be viewed as unconstrained optimization problems on manifold.From this perspective,intrinsic structures,optimality conditions and numerical algorithms for manifold optimization are investigated.Some recent progress on the theoretical results of manifold optimization is also presented.

关 键 词：Convergence First-order-type algorithms Manifold optimization RETRACTION Second-order-type algorithms 

分 类 号：O18[理学—数学]