An Inequality Constrained SL/QP Method for Minimizing the Spectral Abscissa
Abstract
We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest value of the largest real part of the spectrum of a matrix system. This is an important problem for the stabilization of control systems. Many systems require the spectra to lie in the left half plane in order for them to be stable. 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
Cite
@article{arxiv.1411.2362,
title = {An Inequality Constrained SL/QP Method for Minimizing the Spectral Abscissa},
author = {Vyacheslav Kungurtsev and Wim Michiels and Moritz Diehl},
journal= {arXiv preprint arXiv:1411.2362},
year = {2014}
}