Sensitivity analysis of nondifferentiable sums of singular values of rectangular matrices |
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Authors: | Alberto Seeger |
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Affiliation: | Department of Mathematics , University of Avignon , 33, rue Louis Pasteur, Avign1on, 84000, France |
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Abstract: | Let K(x) be an s-by-r rectangular matrix depending on a parameter x ε E and denote by g(x) the sum of its m largest singular values (1 ≤ m ≤ Min{s,r}). If K(x) depends affinely on x, then g is a nondifferentiable convex function. In this paper we consider first the affine case and give some formulas for the conjugate, subdifferential, and ε-subdifferential of g. These formulas are then used to obtain perturbation bounds for g(x). We study next the nonaffine case and discuss some questions related with the regularity, generalized subdifferentiability, and directional differentiability of g. |
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Keywords: | Nondifferentiable matrix function Matrix perturbation Sensitivity of singular values 15A18 49R05 |
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