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Nonsmooth analysis of singular values. II: Applications. (English) Zbl 1129.49026
Summary: In this work we continue the nonsmooth analysis of absolutely symmetric functions of the singular values of a real rectangular matrix [see Part I reviewed above]. Absolutely symmetric functions are invariant under permutations and sign changes of its arguments. We extend previous work on subgradients to analogous formulae for the proximal subdifferential and Clarke subdifferential when the function is either locally Lipschitz or just lower semicontinuous. We illustrate the results by calculating the various subdifferentials of individual singular values. Another application gives a nonsmooth proof of Lidskii’s theorem for weak majorization.

49J52Nonsmooth analysis (other weak concepts of optimality)
90C31Sensitivity, stability, parametric optimization
Full Text: DOI
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