Optimizing Matrix Stability
James V. Burke, Adrian S. Lewis and Michael L. Overton
Given an affine subspace of square matrices, we consider the problem
of minimizing the spectral abscissa (the largest real part of an
eigenvalue). We give an example whose optimal solution has Jordan
form consisting of a single Jordan block, and we show, using
non-lipschitz variational analysis, that this behaviour persists under
arbitrary small perturbations to the example. Thus although matrices
with nontrivial Jordan structure are rare in the space of all
matrices, they appear naturally in spectral abscissa minimization.
NYU Computer Science Dept Technical Report 791.
Submitted to Proceedings of the AMS.