### 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 linearly independent affine constraints on the coefficients. We show that there always exists an optimal polynomial with at most 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.

Original language | English (US) |
---|---|

Pages (from-to) | 509-528 |

Number of pages | 20 |

Journal | Mathematical Programming |

Volume | 165 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2017 |

### Keywords

- Frequency domain stabilization
- Nonsmooth optimization
- Polynomial optimization

### ASJC Scopus subject areas

- Software
- Mathematics(all)

## Fingerprint Dive into the research topics of 'Polynomial root radius optimization with affine constraints'. Together they form a unique fingerprint.

## Cite this

Eaton, J., Grundel, S., Gürbüzbalaban, M., & Overton, M. L. (2017). Polynomial root radius optimization with affine constraints.

*Mathematical Programming*,*165*(2), 509-528. https://doi.org/10.1007/s10107-016-1092-5