Optimization, Complexity and Invariant Theory

Abstract: Sometimes, functions that are non-convex in the Euclidean space turn out to be convex if one introduces a suitable metric on the space and redefines convexity with respect to the straight lines ("geodesics") induced by the metric. Such a function is called "geodesically convex" and, when a function has this property and how to optimize over it, is not well-understood. This talk will introduce geodesic convexity and show that the problem of computing the Brascamp-Lieb constant has a succinct geodesically convex formulation.