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2006.176: Modifying the interia of matrices arising in optimization

2006.176: Nicholas J. Higham and Sheung Hun Cheng (1998) Modifying the interia of matrices arising in optimization. Linear Algebra and its Applications, 275-276. pp. 261-279. ISSN 0024-3795

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DOI: 10.1016/S0024-3795(97)10015-5


Applications in constrained optimization (and other areas) produce symmetric matrices with a natural block 2 × 2 structure. An optimality condition leads to the problem of perturbing the (1,1) block of the matrix to achieve a specific inertia. We derive a perturbation of minimal norm, for any unitarily invariant norm, that increases the number of nonnegative eigenvalues by a given amount, and we show how it can be computed efficiently given a factorization of the original matrix. We also consider an alternative way to satisfy the optimality condition based on a projection approach. Theoretical tools developed here include an extension of Ostrowski's theorem on congruences and some lemmas on inertias of block 2 × 2 symmetric matrices.

Item Type:Article
Uncontrolled Keywords:65F15; 15A42Inertia; Optimization; Nonlinear programming; unitarily invariant norm
Subjects:MSC 2000 > 15 Linear and multilinear algebra; matrix theory
MSC 2000 > 65 Numerical analysis
MIMS number:2006.176
Deposited By:Miss Louise Stait
Deposited On:04 July 2006

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