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A Brief Introduction to Manifold Optimization
Hu Jiang1; Liu Xin2; Wen Zaiwen1; Yuan Yaxiang2
2020
Source PublicationJournal of the Operations Research Society of China
ISSN2194-668X
Volume8Issue:2Pages:199-248
AbstractManifold 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.
KeywordConvergence First-order-type algorithms Manifold optimization Retraction Second-order-type algorithms
Indexed ByCSCD
Language英语
CSCD IDCSCD:6758202
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/53052
Collection中国科学院数学与系统科学研究院
Affiliation1.Beijing International Center for Mathematical Research,Peking University
2.中国科学院数学与系统科学研究院
Recommended Citation
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.
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