Approximating subdifferentials by random sampling of gradients

J. V. Burke, A. S. Lewis, M. L. Overton

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)567-584
Number of pages18
JournalMathematics of Operations Research
Volume27
Issue number3
StatePublished - Aug 2002

Fingerprint

Random Sampling
Subdifferential
Sampling
Gradient
Clarke Subdifferential
Abscissa
Non-Lipschitz
Lipschitz Function
Convex Hull
Differentiable
Euclidean space
Random sampling
Convex hull

Keywords

  • Bundle method
  • Clarke subdifferential
  • Eigenvalue optimization
  • Generalized gradient
  • Nonsmooth analysis
  • Spectral abscissa
  • Stochastic gradient

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Management Science and Operations Research

Cite this

Approximating subdifferentials by random sampling of gradients. / Burke, J. V.; Lewis, A. S.; Overton, M. L.

In: Mathematics of Operations Research, Vol. 27, No. 3, 08.2002, p. 567-584.

Research output: Contribution to journalArticle

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