BLISS Seminar: Geometric optimization: convex and nonconvex
Seminar | April 24 | 4-5 p.m. | 400 Cory Hall
Suvrit Sra, MIT
In this talk, I will highlight some aspects of geometry and its role in optimization. In particular, I will talk about optimization problems whose parameters are constrained to lie on a manifold or in a specific metric space. These geometric constraints often make the problems numerically challenging, but they can also unravel properties that ensure tractable attainment of global optimality for certain otherwise non-convex problems.
We'll make our foray into geometric optimization via geodesic convexity, a concept that generalizes the usual notion of convexity to nonlinear metric spaces such as Riemannian manifolds. I will outline some of our results that contribute to g-convex analysis as well as to the theory of first-order g-convex optimization. I will mention several very interesting optimization problems where g-convexity proves remarkably useful. Time permitting, I will mention extensions to stochastic (non-convex) geometric optimization as well as some important open problems.