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 $Kix\perp (\mathrm{Ax}‐\lambda \mathrm{Bx})\in K^{+}.$. 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.