Polynomial root radius optimization with affine constraints

• 成果类型: Article
• 署名作者: Eaton, Julia; Grundel, Sara; Gurbuzbalaban, Mert; Overton, Michael L.
• 署名单位: University of Washington; University of Washington Tacoma; Max Planck Society; Rutgers University System; Rutgers University New Brunswick; New York University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1092-5
• 发表日期: 2017
• 页码: 509-528
• 关键词: variational analysis; STABILITY; systems; DESIGN; stabilization

摘要

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 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.