Numerical decomposition of a convex function
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Given then×p orthogonal matrixA and the convex functionf:Rn→R, we find two orthogonal matricesP andQ such thatf is almost constant on the convex hull of ± the columns ofP, f is sufficiently nonconstant on the column space ofQ, and the column spaces ofP andQ provide an orthogonal direct sum decomposition of the column space ofA. This provides a numerically stable algorithm for calculating the cone of directions of constancy, at a pointx, of a convex function. Applications to convex programming are discussed.
Key WordsConvex functions convex programming cone of directions of constancy numerical stability
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