Approximation Theory & Convex Optimization

The main goal is to integrate modern optimization techniques (and in particular the Moment-SOS hierarchy) into classical topics in Approximation Theory to advance the state-of-the-art. For instance in the pioneering work "S. Foucart. Computation of Minimal Projections and Extensions, Num. Funct. Anal. Optim., vol 37 (2016)"the determination of minimal projections is examined from an optimization theory viewpoint. It is shown how to transform the problem into appropriate linear programs and obtain approximations that are significantly better than those obtained with more traditional approaches. More recently the same problem has been attacked with the moment-SOS hierarchy to again otain even better approximations. This research program is conducted in collaboration with Simon Foucart (Math. Department, Texas A&M University)