Work

Deflation Techniques for Finding Multiple Local Minima of a Nonlinear Least Squares Problem

Year: 2025

Type: article

Abstract: . In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss–Newton algorithm, and as such do not require the calculation of a Hessian matrix. They also require fewer deflations than for applying the deflated Newton method on the first order optimality conditions, as the latter finds all stationary points, not just local minima. One application of interest covered in this paper is the inverse eigenvalue problem (IEP) associated with the modelling of spectroscopic data of relevance to the physical and chemical sciences. Open source MATLAB code is provided at https://github.com/AlbanBloorRiley/DeflatedGaussNewton . Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/AlbanBloorRiley/DeflatedGaussNewton and in the supplementary materials ( DeflatedGaussNewton-main.zip [29.2KB]). [Formula: see text]

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/24m1695191

Authors: Alban Bloor Riley, Marcus Webb, Michael L. Baker

Institution: University of Manchester

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Manchester, Narodowe Centrum Nauki

Award: G712766103