A nonsmooth algorithm for cone-constrained eigenvalue problems

Abstract

International audienceWe 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