A derivative-free Gauss–Newton method

Author: 

Roberts, L
Cartis, C

Publication Date: 

20 May 2019

Journal: 

Mathematical Programming Computation

Last Updated: 

2020-01-22T13:30:24.107+00:00

Issue: 

4

Volume: 

11

DOI: 

10.1007/s12532-019-00161-7

page: 

631–674-

abstract: 

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 {\mathcal {O}}(\epsilon ^{-2}) iterations to reach approximate first-order criticality within tolerance \epsilon. 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: 

1002910

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article