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A nonsmooth algorithm for cone-constrained eigenvalue problems

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Abstract

We study several variants of a nonsmooth Newton-type algorithm for solving an eigenvalue problem of the form

$$K\ni x\perp(Ax-\lambda Bx)\in K^{+}.$$

Such an eigenvalue problem arises in mechanics and in other areas of applied mathematics. The symbol K refers to a closed convex cone in the Euclidean space ℝn and (A,B) is a pair of possibly asymmetric matrices of order n. Special attention is paid to the case in which K is the nonnegative orthant of ℝn. The more general case of a possibly unpointed polyhedral convex cone is also discussed in detail.

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Authors and Affiliations

  1. XLIM UMR CNRS 6172, Université de Limoges, 123 avenue Albert Thomas, 87060, Limoges, France

    Samir Adly

  2. Département de Mathématiques, Université d’Avignon, 33 rue Louis Pasteur, 84000, Avignon, France

    Alberto Seeger

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  1. Samir Adly
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  2. Alberto Seeger
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Correspondence to Alberto Seeger.

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Adly, S., Seeger, A. A nonsmooth algorithm for cone-constrained eigenvalue problems. Comput Optim Appl 49, 299–318 (2011). https://doi.org/10.1007/s10589-009-9297-7

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