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Article Dans Une Revue Computational Optimization and Applications Année : 2011

A nonsmooth algorithm for cone-constrained eigenvalue problems

Samir Adly
DMI

Résumé

We study several variants of a nonsmooth Newton-type algorithm for solving an eigenvalue problem of the form $K\ni x \bot(Ax−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 $ℝ^n$ 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 $ℝ^n$. The more general case of a possibly unpointed polyhedral convex cone is also discussed in detail.
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Dates et versions

hal-00683026 , version 1 (17-07-2018)

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Samir Adly, Alberto Seeger. A nonsmooth algorithm for cone-constrained eigenvalue problems. Computational Optimization and Applications, 2011, 49 (2), pp.299-318. ⟨10.1007/s10589-009-9297-7⟩. ⟨hal-00683026⟩
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