Nonconvex Analysis

Adil Bagirov (), Napsu Karmitsa () and Marko M. Mäkelä ()
Additional contact information
Adil Bagirov: School of Information Technology and Mathematical Sciences, University of Ballarat
Napsu Karmitsa: University of Turku
Marko M. Mäkelä: University of Turku

Chapter Chapter 3 in Introduction to Nonsmooth Optimization, 2014, pp 61-116 from Springer

Abstract: Abstract In this chapter, we generalize the convex concepts defined in the previous chapter to nonconvex locally Lipschitz continuous functions. Since the classical directional derivative does not necessarily exist for locally Lipschitz continuous functions, we first define a generalized directional derivative. Then we generalize the subdifferential analogously. We use the approach of Clarke in a finite dimensional case. However, in addition to the Clarke subdifferential, many different generalizations of the concept of a subdifferential for nonconvex nonsmooth functions exist. At the end of this chapter we briefly recall some of them. More specifically we give definitions of the quasidifferential, the codifferential, the basic (limiting) and the singular subdifferentials.

Keywords: Nonconvex Analysis; Singular Subdifferential; Clarke Subdifferential; Classical Directional Derivative; Subdifferential Regularity (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-08114-4_3

Ordering information: This item can be ordered from
http://www.springer.com/9783319081144

DOI: 10.1007/978-3-319-08114-4_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().