On the nondifferentiability of cone-monotone functions in Banach spaces

Jonathan Borwein () and Rafal Goebel ()
Additional contact information
Jonathan Borwein: Simon Fraser University
Rafal Goebel: University of California

Chapter Chapter 1 in Optimization, 2009, pp 3-14 from Springer

Abstract: Abstract In finite-dimensional spaces, cone-monotone functions – a special case of which are coordinate-wise nondecreasing functions – possess several regularity properties like almost everywhere continuity and differentiability. Such facts carry over to a separable Banach space, provided that the cone has interior. This chapter shows that further generalizations are not readily possible. We display several examples of cone–monotone functions on various Banach spaces, lacking the regularity expected from their finite-dimensional counterparts.

Keywords: Monotone functions; ordered Banach spaces; generating cones; differentiability (search for similar items in EconPapers)
Date: 2009
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:spochp:978-0-387-98096-6_1

Ordering information: This item can be ordered from
http://www.springer.com/9780387980966

DOI: 10.1007/978-0-387-98096-6_1

Access Statistics for this chapter

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