Polynomial root radius optimization with affine constraints / Julie Eaton, Sara Grundel, Mert Gürbüzbalaban, Michael L. Overton

Abstract

Abstract: The root radius of a polynomial is the maximum of the moduli of its roots (zeros). We consider the following optimization problem: minimize the root radius over monic polynomials of degree n, with either real or complex coefficients, subject to k consistent affine constraints on the coefficients. We show that there always exists an optimal polynomial with at most k − 1 inactive roots, that is, whose modulus is strictly less than the optimal root radius. We illustrate our results using some examples arising in feedback control.