Numerical Decomposition of a Convex Function 1
نویسنده
چکیده
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 decomposi t ion of the column space of A. This provides a numerical ly stable algorithm for calculating the cone of directions of constancy, at a point x, of a convex function. Applicat ions to convex programming are discussed.
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