Abstract
A class of rank-two, inertia-preserving updates for symmetric matricesH c is studied. To ensure that inertia is preserved, the updates are chosen to be of the formH +=FH c F t, whereF=I+qr t, withq andr selected so that the secant equation is satisfied. A characterization is given for all such updates. Using a parameterization of this family of updates, the connection between them and the Broyden class of updates is established. Also, parameter selection criteria that can be used to choose the optimally conditioned update or the update closest to the SR1 update are discussed.
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Communicated by R. A. Tapia
The work of the first author was partially supported by AFOSR Grant 84-0326. The work of the second author was partially supported by NSF Grant EAR-82-18743.
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Beattie, C.A., Boisen, M.B. & Johnson, L.W. Inertia-preserving secant updates. J Optim Theory Appl 62, 1–16 (1989). https://doi.org/10.1007/BF00939626
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DOI: https://doi.org/10.1007/BF00939626