Preprint No. MPIMD/14-24

Title: Polynomial Root Radius Optimization with Affine Constraints

Author(s): Julie Eaton, Sara Grundel, Mert Gürbüzbalaban, Michael Overton


Date: 2014-12-16

Revised: 2015-03-05


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.


author = {Julie Eaton and Sara Grundel and Mert Gürbüzbalaban and Michael Overton},
title = {Polynomial Root Radius Optimization with Affine Constraints},
number = {MPIMD/14-24},
month = dec,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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