Add to ORKGAbstract. 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. Mathematics Subject Classifications (2000): Primary 90C31, 15A18; secondary 49K40, 26B05. Key words: nonsmooth analysis...
AbstractWe prove that any subanalytic locally Lipschitz function has the Sard property. Such functio...
We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are t...
In recent years four subdifferential maps have been widely used: the Clarke subdifferential, the Mic...
Abstract. The singular values of a rectangular matrix are nonsmooth functions of its entries. In thi...
Abstract. For any function f from R to R, one can define a corresponding function on the space of n ...
For any function f from R to R, one can define a corresponding function on the space of n &times...
For any function f from $\mathbb R$ to $\mathbb R$, one can define a corresponding function on the s...
Any spectral function can be written as a composition of a symmetric function $f: \rn \mapsto \Re$ a...
Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be eq...
Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be eq...
We develop a generalized differentiation theory for nonsmooth functions and sets with nonsmooth boun...
We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the...
Author name used in this publication: Xiaoqi Yang2003-2004 > Academic research: refereed > Publicati...
Nonsmooth functions are prevalent. Moreover, during the last decades a number of concepts have been ...
The relationships between the semismoothness of a function and the submonotonicity of its subdiffere...
AbstractWe prove that any subanalytic locally Lipschitz function has the Sard property. Such functio...
We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are t...
In recent years four subdifferential maps have been widely used: the Clarke subdifferential, the Mic...
Abstract. The singular values of a rectangular matrix are nonsmooth functions of its entries. In thi...
Abstract. For any function f from R to R, one can define a corresponding function on the space of n ...
For any function f from R to R, one can define a corresponding function on the space of n &times...
For any function f from $\mathbb R$ to $\mathbb R$, one can define a corresponding function on the s...
Any spectral function can be written as a composition of a symmetric function $f: \rn \mapsto \Re$ a...
Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be eq...
Several kinds of behaviors of extended-real-valued lower semicontinuous functions are known to be eq...
We develop a generalized differentiation theory for nonsmooth functions and sets with nonsmooth boun...
We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the...
Author name used in this publication: Xiaoqi Yang2003-2004 > Academic research: refereed > Publicati...
Nonsmooth functions are prevalent. Moreover, during the last decades a number of concepts have been ...
The relationships between the semismoothness of a function and the submonotonicity of its subdiffere...
AbstractWe prove that any subanalytic locally Lipschitz function has the Sard property. Such functio...
We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are t...
In recent years four subdifferential maps have been widely used: the Clarke subdifferential, the Mic...