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DOI 10.5286/raltr.2019001
Persistent URL http://purl.org/net/epubs/work/40739630
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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
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