Approximating subdifferentials by random sampling of gradients

Approximating subdifferentials by random sampling of gradients

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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: , ,
Abstract:

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.

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