Clarke subgradients of stratifiable functions

Details Clarke subgradients of stratifiable functions Clarke subgradients of stratifiable functions

2006-01-22

arxiv.org/abs/math/0601530v1

Mathematics

Optimization and Control

Scientific paper

We establish the following result: if the graph of a (nonsmooth) real-extended-valued function $f:\mathbb{R}^{n}\to \mathbb{R}\cup\{+\infty\}$ is closed and admits a Whitney stratification, then the norm of the gradient of $f$ at $x\in{dom}f$ relative to the stratum containing $x$ bounds from below all norms of Clarke subgradients of $f$ at $x$. As a consequence, we obtain some Morse-Sard type theorems as well as a nonsmooth Kurdyka-\L ojasiewicz inequality for functions definable in an arbitrary o-minimal structure.

Affiliated with

Also associated with

No associations

Rating

Clarke subgradients of stratifiable functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Clarke subgradients of stratifiable functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Clarke subgradients of stratifiable functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-607301