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

Gould, N. I.M., Rees, T. and Scott, J. (2019) Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems. Computational Optimization and Applications, 73 (1). pp. 1-35. ISSN 0926-6003

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To link to this item DOI: 10.1007/s10589-019-00064-2

Abstract/Summary

Given a twice-continuously differentiable 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. Numerical experiments comparing tensor-Newton methods with regularized Gauss-Newton and Newton methods demonstrate the practical performance of the newly proposed method.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:82226
Publisher:Springer

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