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Clarke critical values of subanalytic Lipschitz continuous functions

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Bolte J., Daniilidis A., Lewis A., Shiota M.

Annales Polonici Mathematici

2005

tom 87

nr 1

13-25

The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawłucki's extension of the Puiseux lemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

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1 Annales Polonici Mathematici

1 Bolte J.

1 Daniilidis A.

1 Lewis A.

1 Shiota M.

1 2005

Wyniki wyszukiwania

Clarke critical values of subanalytic Lipschitz continuous functions