Optimization Online


Approximating Subdifferentials by Random Sampling of Gradients

James V. Burke (burke***at***math.washington.edu)
Adrian S. Lewis (aslewis***at***cecm.sfu.ca)
Michael L. Overton (overton***at***cs.nyu.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.

Download: [Postscript]

Entry Submitted: 05/31/2001
Entry Accepted: 05/31/2001
Entry Last Modified: 05/31/2001

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society