SCO Seminar - Amir Shakouri, University of Groningen

Title: Chebyshev Centers and Radii for Sets Induced by Quadratic Matrix Inequalities

Abstract:

In this colloquium, we present our recent research results on sets of matrices induced by quadratic inequalities. In particular, we focus on the center and radius of a smallest ball containing the set, called a Chebyshev center and the Chebyshev radius. We also study the diameter of the set, which is the farthest distance between any two elements of the set. Closed-form solutions are provided for a Chebyshev center, the Chebyshev radius, and the diameter of sets induced by quadratic matrix inequalities (QMIs) with respect to arbitrary unitarily invariant norms. Examples of these norms include the Frobenius norm, spectral norm, nuclear norm, Schatten p-norms, and Ky Fan k-norms. In addition, closed-form solutions are provided for the radius of the largest ball within a QMI-induced set.