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

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DOI	10.5286/raltr.2019001
Persistent URL	http://purl.org/net/epubs/work/40739630
Record Status	Checked
Record Id	40739630
Title	Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems subject to convex constraints
Contributors	NIM Gould (STFC Rutherford Appleton Lab.), T Rees (STFC Rutherford Appleton Lab.), JA Scott (STFC Rutherford Appleton Lab.)
Abstract	Given a twice-continuously diﬀerentiable vector-valued function r(x), a local minimizer of∥r(x)∥2 within a convex set 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 constrained 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. Numerical experiments comparing tensor-Newton methods with regularized Gauss-Newton and Newton methods demonstrate the practical performance of the newly proposed method in the unconstrained case.
Organisation	STFC , SCI-COMP
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Licence Information:	Creative Commons Attribution 4.0 International (CC BY 4.0)
Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Technical Reports RAL-TR-2019-001. STFC, 2019.		RAL-TR-2019-001.pdf	2019