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A tensor trust-region model for nonlinear system.

作者信息

Wang Songhua, Liu Shulun

机构信息

1School of Mathematics and Statistics, Baise University, Baise, P.R. China.

Department of Information Engineering, Jiyuan Vocational and Technical College, Henan, P.R. China.

出版信息

J Inequal Appl. 2018;2018(1):343. doi: 10.1186/s13660-018-1935-0. Epub 2018 Dec 13.

DOI:10.1186/s13660-018-1935-0
PMID:30839853
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6291438/
Abstract

It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric tensor trust-region subproblem model of the nonlinear equations is presented; (ii) the three dimensional symmetric tensor is replaced by interpolating function and gradient values from the most recent past iterate, which avoids the storage of the three dimensional symmetric tensor and decreases the workload of the computer; (iii) the limited BFGS quasi-Newton update is used instead of the second Jacobian matrix, which generates an inexpensive computation of a complex system; (iv) the global convergence is proved under suitable conditions. Numerical experiments are done to show that this proposed algorithm is competitive with the normal algorithm.

摘要
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/678f677a5023/13660_2018_1935_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/b0866b1510e8/13660_2018_1935_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/9f496baea9ff/13660_2018_1935_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/678f677a5023/13660_2018_1935_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/b0866b1510e8/13660_2018_1935_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/9f496baea9ff/13660_2018_1935_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6e66/6291438/678f677a5023/13660_2018_1935_Fig3_HTML.jpg

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本文引用的文献

1
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.两种用于最小化优化模型的新型PRP共轭梯度算法。
PLoS One. 2015 Oct 26;10(10):e0140071. doi: 10.1371/journal.pone.0140071. eCollection 2015.
2
A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations.
PLoS One. 2015 May 7;10(5):e0120993. doi: 10.1371/journal.pone.0120993. eCollection 2015.