Derivative-free optimisation for least-squares problems

Abstract: 

Least-squares problems (such as parameter estimation) are ubiquitous across quantitative disciplines. Optimisation algorithms for solving such problems are numerous and well-established. However, in cases where models are computationally expensive, black box, or noisy, classical algorithms can be impractical or even fail. Derivative-free optimisation (DFO) methods provide an alternative approach which can handle these settings. In this talk, Lindon will introduce a derivative-free version of the classical Gauss-Newton method, discuss its theoretical guarantees and software implementation, and describe applications of this technique to parameter estimation of global climate models and image reconstruction.

Lindon Roberts is an MSI Fellow at the Mathematical Sciences Institute at the Australian National University. His research focuses on the development, theoretical analysis and implementation of algorithms for nonlinear optimisation. His paper "A derivative-free Gauss-Newton method" shared the 2019 best paper award for Mathematical Programming Computation, and his software has been included in the NAG Library of numerical algorithms.