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

Nicholas I. M. Gould (), Tyrone Rees () and Jennifer A. Scott ()
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Nicholas I. M. Gould: STFC Rutherford Appleton Laboratory
Tyrone Rees: STFC Rutherford Appleton Laboratory
Jennifer A. Scott: STFC Rutherford Appleton Laboratory

Computational Optimization and Applications, 2019, vol. 73, issue 1, No 1, 35 pages

Abstract: Abstract Given a twice-continuously differentiable vector-valued function r(x), a local minimizer of $$\Vert r(x)\Vert _2$$ ‖ 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 $$\Vert r(x)\Vert _2$$ ‖ 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.

Keywords: Nonlinear least-squares; Levenberg Marquardt; Trust region methods; Data fitting (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-019-00064-2

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