Optimizing matrix stability

被引：29

作者：

Burke, JV ^{[1
]}

Lewis, AS

Overton, ML

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada

[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 06期

关键词：

eigenvalue optimization; spectral abscissa; nonsmooth analysis; Jordan form;

D O I：

10.1090/S0002-9939-00-05985-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 nonlipschitz 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.

引用

页码：1635 / 1642

页数：8