Sum-of-Squares Approximation Hierarchies for Polynomial Optimization

Abstract: Minimizing a polynomial function over a compact set is a computationally hard problem, already when restricting to quadratic polynomials and to simple sets like a ball, a hypercube, or a simplex. We discuss some hierarchies of bounds introduced by Lasserre, that are based on searching for an optimal sum-of-squares density function minimizing the expected value of f over K.

We will discuss several techniques that permit to analyse the performance guarantee of these bounds depending on the degree of the sum-of-square density. This includes using an eigenvalue reformulation of the bounds, links to extremal roots of orthogonal polynomials, and reducing to the univariate case by means of push-forward measures.

Based on joint works with Etienne de Klerk and Lucas Slot.

optimization and control

Audience: researchers in the discipline

Comments: The address and password of the zoom room of the seminar are sent by e-mail on the mailinglist of the seminar one day before each talk

---

One World Optimization seminar

Series comments: Description: Online seminar on optimization and related areas

The address and password of the zoom room of the seminar are sent by e-mail on the mailinglist of the seminar one day before each talk

---