Optimizing matrix stability
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- by J. V. Burke, A. S. Lewis and M. L. Overton PDF
- Proc. Amer. Math. Soc. 129 (2001), 1635-1642 Request permission
Abstract:
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.References
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Additional Information
- J. V. Burke
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- Email: burke@math.washington.edu
- A. S. Lewis
- Affiliation: Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- Email: aslewis@math.uwaterloo.ca
- M. L. Overton
- Affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
- Email: overton@cs.nyu.edu
- Received by editor(s): September 28, 1999
- Published electronically: October 31, 2000
- Additional Notes: The first author’s research was supported by the National Science Foundation grant number DMS-9971852
The second author’s research was supported by the Natural Sciences and Engineering Research Council of Canada
The third author’s research was supported by the National Science Foundation grant number CCR-9731777, and the U.S. Department of Energy Contract DE-FG02-98ER25352 - Communicated by: Jonathan M. Borwein
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1635-1642
- MSC (2000): Primary 15A42, 90C30; Secondary 65F15, 49K30
- DOI: https://doi.org/10.1090/S0002-9939-00-05985-2
- MathSciNet review: 1814091