A derivative-free Gauss–Newton method

Author: 

Cartis, C
Roberts, L

Publication Date: 

1 January 2019

Journal: 

Mathematical Programming Computation

Last Updated: 

2020-01-21T09:14:08.91+00:00

DOI: 

10.1007/s12532-019-00161-7

abstract: 

© 2019, The Author(s). 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(ϵ- 2) iterations to reach approximate first-order criticality within tolerance ϵ. 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).

Symplectic id: 

890917

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article