Julia Eaton, Sara Grundel, Mert Gürbüzbalaban, Michael Overton
Polynomial root radius optimization with affine constraints J Eaton, S Grundel, M Gürbüzbalaban, ML Overton - Mathematical Programming, 2017
Publication year: 2017

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 linearly
independent affine constraints on the coefficients. We show that there always exists an
optimal polynomial with at most k-1 k-1 inactive roots, that is, roots whose moduli are strictly
less than the optimal root radius. We illustrate our results using some examples arising in
feedback control.