Skip to main content

Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient

  • Chapter
Minimization Methods for Non-Differentiable Functions

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 3))

  • 1362 Accesses

Abstract

When solving many mathematical programming problems one has to consider a broader class of functions than that of continuously differentiable functions. In such cases We, as a rule, deal with continuous and almost everywhere differentiable functions, whose gradient is discontinuous on a set of null measure. Although in principle functions may arise with even greater pathology (for example, functions that are nowhere differentiable on a set of positive measure), such functions are not encountered in practice; moreover, construction of any nontrivial algorithm for minimizing such functions does not appear possible.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin, Heidelberg

About this chapter

Cite this chapter

Shor, N.Z. (1985). Special Classes of Nondifferentiable Functions and Generalizations of the Concept of the Gradient. In: Minimization Methods for Non-Differentiable Functions. Springer Series in Computational Mathematics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82118-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-82118-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82120-2

  • Online ISBN: 978-3-642-82118-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics