Abstract

Real-life applications often require the optimization of nonlinear functions with several unknowns or parameters - where the function is the result of highly expensive and complex model simulations involving noisy data (such as climate or financial models, chemical experiments), or the output of a black-box or legacy code, that prevent the numerical analyst from looking inside to find out or calculate problem information such as derivatives. Thus classical optimization algorithms, that use derivatives (steepest descent, Newton's methods) often fail or are entirely inapplicable in this context. Efficient derivative-free optimization algorithms have been developed in the last 15 years in response to these imperative practical requirements. As even approximate derivatives may be unavailable, these methods must explore the landscape differently and more creatively. In state of the art techniques, clouds of points are generated judiciously and sporadically updated to capture local geometries as inexpensively as possible; local function models around these points are built using techniques from approximation theory and carefully optimised over a local neighbourhood (a trust region) to give a better solution estimate.

In this talk, I will describe our implementations and improvements to state-of-the-art methods. In the context of the ubiquitous data fitting/least-squares applications, we have developed a simplified approach that is as efficient as state of the art in terms of budget use, while achieving better scalability. Furthermore, we substantially improved the robustness of derivative-free methods in the presence of noisy evaluations. Random-subspace variants of these methods yield further substantial improvements to their scalability. Theoretical guarantees of the different methods will also be provided. 

Biography

Coralia Cartis is Professor of Numerical Optimization at the Mathematical Institute, University of Oxford and a Fellow of Balliol College and The Alan Turing Institute for Data Science. She received a BSc degree in mathematics from Babesh-Bolyai University, Cluj-Napoca, Romania, and a PhD degree in mathematics from the University of Cambridge, under the supervision of Prof Michael J.D. Powell. Prior to her current post, she worked as a research scientist at Rutherford Appleton Laboratory and as a postdoctoral researcher at Oxford University, and was a tenured assistant professor in the School of Mathematics, University of Edinburgh. Her research interests include the development and analysis of nonlinear optimization algorithms and diverse applications of optimization from climate modeling to signal processing and machine learning. She serves on the editorial boards of leading optimization and numerical analysis journals and was awarded some prizes for her research.