A Brief Introduction to Manifold Optimization

CSpace

	A Brief Introduction to Manifold Optimization
	Hu Jiang 1; Liu Xin 2; Wen Zaiwen 1; Yuan Yaxiang 2
	2020
发表期刊	Journal of the Operations Research Society of China
ISSN	2194-668X
卷号	8 期号:2 页码:199-248
摘要	Manifold optimization is ubiquitous in computational and applied mathematics, 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
收录类别	CSCD
语种	英语
CSCD记录号	CSCD:6758202
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/53052
专题	中国科学院数学与系统科学研究院
作者单位	1.Beijing International Center for Mathematical Research,Peking University 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Hu Jiang,Liu Xin,Wen Zaiwen,et al. A Brief Introduction to Manifold Optimization[J]. Journal of the Operations Research Society of China,2020,8(2):199-248.
APA	Hu Jiang,Liu Xin,Wen Zaiwen,&Yuan Yaxiang.(2020).A Brief Introduction to Manifold Optimization.Journal of the Operations Research Society of China,8(2),199-248.
MLA	Hu Jiang,et al."A Brief Introduction to Manifold Optimization".Journal of the Operations Research Society of China 8.2(2020):199-248.