Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems

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Persistent URL	http://purl.org/net/epubs/work/36041894
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Record Id	36041894
Title	Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems
Contributors	NIM Gould (STFC Rutherford Appleton Lab.), T Rees (STFC Rutherford Appleton Lab.), JA Scott (STFC Rutherford Appleton Lab.)
Abstract	Given a twice-continuously vector-valued function r(x), a local minimizer of ∥r(x)∥2 is sought. We propose and analyse tensor-Newton methods, in which r(x) is replaced locally by its second-order Taylor approximation. Convergence is controlled by regularization of various orders. We establish global convergence to a first-order critical point of ∥r(x)∥2, and provide function evaluation bounds that agree with the best-known bounds for methods using second derivatives.
Organisation	STFC , SCI-COMP
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	RAL Preprints RAL-P-2017-009, Computational Optimization and Applications STFC, 2017.		RAL-P-2017-009.pdf	2017