Optimizing matrix stability |
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| Authors: | J V Burke A S Lewis M L Overton |
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| Institution: | Department of Mathematics, University of Washington, Seattle, Washington 98195 ; Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ; Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 |
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| 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. |
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| Keywords: | Eigenvalue optimization spectral abscissa nonsmooth analysis Jordan form |
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