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Volume 17, Issue 2
New Kantorovich’s Theorems for Newton’s Method on Lie Groups for Mappings and Matrix Optimization Problems

Li Nan

J. Info. Comput. Sci. , 17 (2022), pp. 154-160.

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  • Abstract

We propose a new Kantorovich theorem for Newton's method on Lie groups for mappings and matrix low-rank optimization problems, which arises from many applications. Under the classical hypothesis of f, we establish the convergence criteria of Newton's method from Lie group to its Lie algebra with weakened conditions, which improves the corresponding results in [20].

  • Keywords

Lie group, Newton’s method, Trace function, Lipschitz condition.

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COPYRIGHT: © Global Science Press

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@Article{JICS-17-154, author = {Nan , Li}, title = { New Kantorovich’s Theorems for Newton’s Method on Lie Groups for Mappings and Matrix Optimization Problems}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {17}, number = {2}, pages = {154--160}, abstract = {

We propose a new Kantorovich theorem for Newton's method on Lie groups for mappings and matrix low-rank optimization problems, which arises from many applications. Under the classical hypothesis of f, we establish the convergence criteria of Newton's method from Lie group to its Lie algebra with weakened conditions, which improves the corresponding results in [20].

}, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22356.html} }
TY - JOUR T1 - New Kantorovich’s Theorems for Newton’s Method on Lie Groups for Mappings and Matrix Optimization Problems AU - Nan , Li JO - Journal of Information and Computing Science VL - 2 SP - 154 EP - 160 PY - 2024 DA - 2024/01 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22356.html KW - Lie group, Newton’s method, Trace function, Lipschitz condition. AB -

We propose a new Kantorovich theorem for Newton's method on Lie groups for mappings and matrix low-rank optimization problems, which arises from many applications. Under the classical hypothesis of f, we establish the convergence criteria of Newton's method from Lie group to its Lie algebra with weakened conditions, which improves the corresponding results in [20].

Nan , Li. (2024). New Kantorovich’s Theorems for Newton’s Method on Lie Groups for Mappings and Matrix Optimization Problems. Journal of Information and Computing Science. 17 (2). 154-160. doi:
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