Article ID: | iaor2004770 |
Country: | United States |
Volume: | 27 |
Issue: | 3 |
Start Page Number: | 567 |
End Page Number: | 584 |
Publication Date: | Aug 2002 |
Journal: | Mathematics of Operations Research |
Authors: | Burke J.V., Lewis A.S., Overton M.L. |
Many interesting real functions on Euclidean space are differential almost everywhere. All Lipschitz functions have this property, but so, for example, does the spectral abscissa of a mixture (a non-Lipschitz function). In practice, the gradient is often easy to compute. We investigate to what extent we can approximate the Clarke subdifferential of such a function at some point by calculating the convex hull of some gradients sampled at random nearby points.