Numerical decomposition of a convex function

Abstract

Abstract. Given the n x p orthogonal matrix A and the convex function f : R"-~ R, we find two orthogonal matrices P and Q such that f is almost constant on the convex hull of ± the columns of P, f is sufficiently nonconstant on the column space of Q, and the column spaces of P and Q provide an orthogonal direct sum decomposition of the column space of A. This provides a numerically stable algorithm for calculating the cone of directions of constancy, at a point x, of a convex function. Applications to convex programming are discussed.