Approximating Subdifferentials by Random Sampling of Gradients
James V. Burke (burkemath.washington.edu)
Abstract: Many interesting real functions on Euclidean space are differentiable almost everywhere. All Lipschitz functions have this property, but so, for example, does the spectral abscissa of a matrix (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.
Keywords: Spectral abscissa, spectral radius, nonsmooth analysis
Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )
Citation: Submitted to Math. Oper. Research.
Entry Submitted: 05/31/2001
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