SEMIDEFINITE PROGRAMMING FOR THE NEAREST HURWITZ SEMIDEFINITE MATRIX PROBLEM

Suliman Al-Homidan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Polynomials with zeroes in the open left half-plane of the complex plane are called Hurwitz stable. They correspond to Hurwitz matrices which arise in many important applications. A polynomial is Hurwitz stable when the Hurwitz matrix is positive semidefinite. This paper construct structured Hurwitz positive semidefinite matrix that is nearest to a given data matrix. The problem is converted into a semidefinite programming problem as well as a problem comprising of semidefined program and second-order cone problem. The duality and optimality conditions are obtained and the primal-dual algorithm is outlined. Some of the numerical issues involved will be addressed including unsymmetrical of the problem. Computational results are presented.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Nonlinear and Convex Analysis
Volume25
Issue number1
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 Yokohama Publications. All rights reserved.

Keywords

  • Conjugate gradients methods
  • Hurwitz matrix
  • Hurwitz polynomials
  • Inexact Gauss-Newton method
  • non-smooth optimization
  • positive semidefinite matrix
  • primal-dual interior point method
  • semidefinite programming

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

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