A nonsmooth algorithm for cone-constrained eigenvalue problems
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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