Nonsmooth Analysis of Singular Values. Part II: Applications
Nonsmooth Analysis of Singular Values. Part II: Applications
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DOI：
10.1007/s11228-004-7198-6
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发表时间：
2005-09
期刊：
影响因子：
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通讯作者：
A. Lewis;Hristo S. Sendov
中科院分区：
文献类型：
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作者：
A. Lewis;Hristo S. Sendov
本文继续讨论了真实的矩形矩阵奇异值的绝对对称函数的非光滑性。绝对对称函数在变元置换和变号下不变。我们以前的工作次梯度类似公式的近端次微分和克拉克次微分时，功能是局部Lipschitz或只是较低的连续。我们通过计算单个奇异值的各种次微分来说明结果。另一个应用给出了Lidskii弱控制定理的非光滑证明。
In this work we continue the nonsmooth analysis of absolutely symmetric functions of the singular values of a real rectangular matrix. 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.