Department of Mathematical Sciences
Adrian Lewis, Cornell University
Thursday, April 9th, 2026
2:00PM-2:50PM
Salisbury Laboratories 104
Speaker: Adrian Lewis, Cornell University
Title: First-order optimization without (much) geometry
Abstract: Contemporary optimization algorithms and their machine learning applications rely on derivative-like information for objectives. Unlike the classical setting of smooth or convex functions on Euclidean space, complexity analysis for modern algorithms must rely on milder or less familiar geometric foundations. Objectives may be semi-algebraic, as in popular KurdykaLojasiewicz-style analyses, or (in a 2020 method of Zhang et al. ) merely Lipschitz. Furthermore, rather than Euclidean space, the data and variables may live in manifolds, like hyperbolic space or the positive-definite matrices, or in more general nonpositively-curved geodesic spaces, like BHV-tree-space phylogenetic models. This talk, which relies on no optimization background, presents a sequence of short snapshots of this new arena.
Joint work with A. Goodwin, Siyu Kong, G. Lopez, A. Nicolae, and Tonghua Tian.