Title: The Geometry of Nonsmooth Optimization
| Speaker: | Adrian Lewis |
| Affiliation: | Cornell University |
| Location: | MC 5501 |
Abstract:
Von Neumann's alternating projections algorithm for intersecting sets enduringly captures several core ideas for continuous optimization: linear convergence rates, sensitivity, computational error bounds and numerical robustness all unify through the geometry of transversality. In general semi-algebraic optimization settings, transversality holds generically, and perturbation reveals the active manifolds central to classical theory. I illustrate with examples from eigenvalue optimization and polynomial stability in control systems, and a prox-linear algorithm for large-scale composite optimization in machine learning.
Joint work with: J. Bolte, A. Daniilidis, A. Dontchev, D. Drusvyatskiy, A. Ioffe, M. Overton, T. Rockafellar, S. Wright