Optimization Online



Vyacheslav Kungurtsev(vyacheslav.kungurtsev***at***cs.kuleuven.be)
Wim Michiels(wim.michiels***at***cs.kuleuven.be)
Moritz Diehl(moritz.diehl***at***imtek.uni-freiburg.de)

Abstract: We consider a problem in eigenvalue optimization, in particular find- ing a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest magnitude of the largest real part of the spectrum of a matrix system. This is an important problem for the stabilization of control sys- tems. Many systems require the spectra to lie in the left half plane in order for stability to hold. The optimization problem, however, is difficult to solve because the underlying objective function is nonconvex, nonsmooth, and non-Lipschitz. In addition, local minima tend to correspond to points of non-differentiability and locally non-Lipschitz behavior. We present a sequential linear and quadratic programming algorithm that solves a series of linear or quadratic subproblems formed by linearizing the surfaces corresponding to the largest eigenvalues. We present numerical results comparing the algorithms to the state of the art.

Keywords: Robust control, stabilizing control, eigenvalue optimization, spectral abscissa, sequential quadratic programming, spectral optimization, nonlinear eigenvalue problem

Category 1: Applications -- Science and Engineering (Control Applications )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Submitted to ESAIM

Download: [PDF]

Entry Submitted: 05/09/2014
Entry Accepted: 05/09/2014
Entry Last Modified: 05/09/2014

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society