A derivative-free Gauss–Newton method

  • We present DFO-GN, a derivative-free version of the Gauss–Newton method for solving nonlinear least-squares problems. DFO-GN uses linear interpolation of residual values to build a quadratic model of the objective, which is then used within a typical derivative-free trust-region framework. We show that DFO-GN is globally convergent and requires at most O(??2) iterations to reach approximate first-order criticality within tolerance ?. We provide an implementation of DFO-GN and compare it to other state-of-the-art derivative-free solvers that use quadratic interpolation models. We demonstrate numerically that despite using only linear residual models, DFO-GN performs comparably to these methods in terms of objective evaluations. Furthermore, as a result of the simplified interpolation procedure, DFO-GN has superior runtime and scalability. Our implementation of DFO-GN is available at https://github.com/numericalalgorithmsgroup/dfogn (https://doi.org/10.5281/zenodo.2629875).

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Coralia Cartis, Lindon Roberts
DOI:https://doi.org/10.1007/s12532-019-00161-7
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2019
Tag:Software; Theoretical Computer Science
Volume:11
Issue:4
Page Number:44
First Page:631
Last Page:674
Mathematical Programming Computation :MPC 2019 - Issue 4
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.