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Polynomial Root Radius Optimization with Affine Constraints

Julia Eaton (jreaton***at***uw.edu)
Sara Grundel (grundel***at***mpi-magdeburg.mpg.de)
Mert Gurbuzbalaban (mertg***at***mit.edu)
Michael L. Overton (mo1***at***nyu.edu)

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.

Keywords: polynomial optimization, nonsmooth optimization, frequency domain stabilization

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Category 3: Other Topics

Citation: 2015-03-4808, Eaton: Interdisciplinary Arts & Sciences, University of Washington Tacoma, Tacoma, WA 98402; Grundel: Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany; Gurbuzbalaban: Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Boston, MA 02139; Overton: Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, March/2015

Download: [PDF]

Entry Submitted: 03/06/2015
Entry Accepted: 03/06/2015
Entry Last Modified: 03/06/2015

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