Lindon Roberts is an MSI Fellow at the Mathematical Sciences Institute, Australian National University. His research interests are in numerical analysis and data science, particularly nonconvex and derivative-free optimization.
PhD in Mathematics, 2020 (passed, not yet awarded)
University of Oxford
Bachelor of Computational Sciences (Honours), 2011
Australian National University
Optimization—finding the maximum or minimum of a function—is one of the most important classes of problem in computational mathematics, arising often in scientific and industrial applications. My focus is on nonlinear optimization, where the function to be optimized (the ‘objective’ function) is some nonlinear, nonconvex function with unknown structure.
Generally speaking, to optimize a nonlinear objective, you approximate it locally by some simpler function (such as a low-order Taylor series). To construct this simpler function, you need to evaluate the objective and its derivatives at some set of points. Evaluating the derivative of the objective can be done in several ways:
However, if the objective is black-box, expensive to evaluate or noisy (e.g. a Monte Carlo simulation, or involves the finite termination of an iterative procedure), these approaches may be impractical or inaccurate. Derivative-free optimization (DFO) is the field devoted to nonlinear optimization of objectives when you only have access to (possibly inaccurate) evaluations of the objective.
My research
I develop and study model-based DFO algorithms. This is a class of DFO method which tries to incorporate features of derivative-based methods, and ultimately build local approximations to the objective (e.g. by polynomial interpolation). I have developed several algorithms and software packages for solving least-squares problems with DFO methods, and developed techniques which make model-based DFO more robust to noise, able to local minima, and tackle large-scale problems via dimensionality reduction.
[2019 – present] MSI Fellow, Australian National University
[2015 – 2019] Doctoral Student, University of Oxford
[2012 – 2015] Senior Analyst, Macquarie Group
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Australian National University
University of Oxford
Qualifications