Derivative-Free Optimisation Methods for Nonlinear Least-Squares Problems

Abstract

Derivative-free optimisation (DFO) algorithms are a category of optimisation methods for situations when one is unable to compute or estimate derivatives of the objective. The need for DFO arises in applications where techniques such as finite differencing or algorithmic differentiation are inaccurate or impractical, such as when the objective has noise (e.g. Monte Carlo simulations in finance) or is very expensive (e.g. climate simulations).

In this talk I will present a flexible derivative-free Gauss-Newton framework for unconstrained nonlinear least-squares problems. This framework is a simplification and improvement over state-of-the-art model-based trust region DFO methods for nonlinear least-squares [Zhang, Conn & Scheinberg, SIAM J. Optim., 20 (2010), 3555-3576]. Time permitting, I will discuss particular features of this framework, such as a low initialisation cost (in terms of objective evaluations) and improved performance for stochastic problems.

Lindon Roberts

Lecturer

My research is in numerical analysis and data science, particularly nonconvex and derivative-free optimization.