Randomized subspace methods for high-dimensional model-based derivative-free optimization (35mins)

Abstract

Derivative-free optimization (DFO) is the mathematical study of optimization algorithms that do not use derivatives.  Model-based DFO methods are widely used in practice but are known to struggle in high dimensions.  This talk provides a brief overview of recent research, covering both unconstrained and convex-constrained optimization problems, that addresses this issue by searching for decreases within randomly sampled low-dimensional subspaces.  In particular, we examine the requirements for model accuracy and subspace quality in these methods, and compare their convergence guarantees and complexity bounds.  This talk concludes with a discussion of some promising future directions in this area.

Yiwen Chen

PhD student in Mathematics

My research interests include derivative-free optimization, numerical optimization, and discrete geometry.