Three Uses of Semidefinite Programming in Approximation Theory

Data Science Seminar

Simon Foucart (Texas A & M University)

You may attend the talk either in person in Walter 402 or register via Zoom. Registration is required to access the Zoom webinar.

In this talk, modern optimization techniques are publicized as fitting computational tools to attack several extremal problems from Approximation Theory which had reached their limitations based on purely analytical approaches. Three such problems are showcased: the first problem---minimal projections---involves minimization over measures and exploits the moment method; the second problem---constrained approximation---involves minimization over polynomials and exploits the sum-of-squares method; and the third problem---optimal recovery from inaccurate observations---is highly relevant in Data Science and exploits the S-procedure. In each of these problems, one ends up having to solve semidefinite programs.