A nonsmooth algorithm for cone-constrained eigenvalue problems

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 ? 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 ? ⁿ . The more general case of a possibly unpointed polyhedral convex cone is also discussed in detail.