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On the nondifferentiability of cone-monotone functions in Banach spaces

In: Optimization

Author

Listed:
  • Jonathan Borwein

    (Simon Fraser University)

  • Rafal Goebel

    (University of California)

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.

Suggested Citation

  • Jonathan Borwein & Rafal Goebel, 2009. "On the nondifferentiability of cone-monotone functions in Banach spaces," Springer Optimization and Its Applications, in: Charles Pearce & Emma Hunt (ed.), Optimization, edition 1, chapter 0, pages 3-14, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-98096-6_1
    DOI: 10.1007/978-0-387-98096-6_1
    as

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