Math & Stats Colloquium Series - Nov. 14, 2025 (Dr. Warren Hare)

Speaker: Dr. Warren Hare

Title:  Cosine Measures and Derivative Free Optimization

Abstract: 

A positive spanning set (PSS) is a set that contains vectors pointing into every half-space. This provides the exact property required to ensure convergence for certain derivative free optimization algorithms. The quality of a PSS can be studied via the cosine measure. In this talk, we discuss the cosine measure, what it captures, how to compute it, and some of the remaining challenges linked to its mathematics.

• This talk aims to be accessible to anyone with a firm understanding of multivariate calculus and linear algebra.

Bio: Dr. Warren Hare received his PhD in Mathematical Optimization from Simon Fraser University. He joined UBC Okanagan in 2009, where he is currently a Professor in the Department of Computer Science, Mathematics, Physics and Statistics. His research in derivative-free optimization — spanning both theory and applications — focuses on developing smarter ways to find better ways to advance the methods to push the boundaries of solving blackbox problem. He serves as an Associate Editor for Set-Valued and Variational Analysis and the Pacific Journal of Optimization. He is also co-author of the book Derivative-Free and Blackbox Optimization, with the second edition scheduled for release this winter.