DFBGN: Derivative-Free Block Gauss-Newton Optimizer for Least-Squares Minimization

Release: 0.1

Date: 25 February 2021

Author: Lindon Roberts

DFBGN is a package for finding local solutions to large-scale nonlinear least-squares minimization problems, without requiring any derivatives of the objective. DFBGN stands for Derivative-Free Block Gauss-Newton.

That is, DFBGN solves

\[\min_{x\in\mathbb{R}^n} \quad f(x) := \sum_{i=1}^{m}r_{i}(x)^2\]

Full details of the DFBGN algorithm are given in our paper: Coralia Cartis and Lindon Roberts, Scalable Subspace Methods for Derivative-Free Nonlinear Least-Squares Optimization, arXiv preprint arXiv:2102.12016, (2021).

If you wish to solve small-scale least-squares problems, you may wish to try DFO-LS. If you are interested in solving general optimization problems (without a least-squares structure), you may wish to try Py-BOBYQA.

DFBGN is released under the GNU General Public License. Please contact NAG for alternative licensing.

Contents:

• Installing DFBGN
  • Requirements
  • Installation using pip
  • Manual installation
  • Testing
  • Uninstallation
• Using DFBGN
  • Nonlinear Least-Squares Minimization
  • How to use DFBGN
  • A Simple Example
  • More Output
  • Example: Noisy Objective Evaluation
  • Example: Solving a Nonlinear System of Equations
  • References

Acknowledgements

This software was developed under the supervision of Coralia Cartis, and was supported by the EPSRC Centre For Doctoral Training in Industrially Focused Mathematical Modelling (EP/L015803/1) in collaboration with the Numerical Algorithms Group.