Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems
| Autor: | Nicholas I. M. Gould, Tyrone Rees, Jennifer A. Scott |
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| Rok vydání: | 2019 |
| Předmět: |
021103 operations research
Control and Optimization Applied Mathematics 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology Function (mathematics) 01 natural sciences Regularization (mathematics) Levenberg–Marquardt algorithm Computational Mathematics symbols.namesake Non-linear least squares Convergence (routing) Taylor series symbols Applied mathematics Differentiable function 0101 mathematics Newton's method Mathematics |
| Zdroj: | Computational Optimization and Applications. 73:1-35 |
| ISSN: | 1573-2894 0926-6003 |
| DOI: | 10.1007/s10589-019-00064-2 |
| Popis: | Given a twice-continuously differentiable vector-valued function r(x), a local minimizer of $$\Vert r(x)\Vert _2$$ 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 $$\Vert r(x)\Vert _2$$ , 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. |
| Databáze: | OpenAIRE |
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