Abstract
Given then×p orthogonal matrixA and the convex functionf:R n→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.
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Communicated by A. V. Fiacco
This work was supported by the National Science and Engineering Research Council of Canada (Grant No. A3388 and Summer Grant).
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Lamoureux, M., Wolkowicz, H. Numerical decomposition of a convex function. J Optim Theory Appl 47, 51–64 (1985). https://doi.org/10.1007/BF00941315
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DOI: https://doi.org/10.1007/BF00941315