Monotonic analysis over cones: I

J. Dutta, J. E. Martínez-Legaz, A. M. Rubinov

Research output: Contribution to journalArticleResearchpeer-review

23 Citations (Scopus)

Abstract

In this article, we study increasing and positively homogeneous functions defined on convex cones of locally convex spaces. This work is the first part in a series of studies to have a general view of the emerging area of Monotonic Analysis. We develop a general notion of so-called elementary functions, so that the generalized increasing and positively homogeneous functions can be represented as upper-envelopes of families of such functions. We also study many other associated properties like the description of support sets and normal and co-normal sets in a very general setting.
Original languageEnglish
Pages (from-to)129-146
JournalOptimization
Volume53
DOIs
Publication statusPublished - 1 Apr 2004

Keywords

  • Abstract convexity
  • Co-normal sets
  • IPH functions
  • Monotonie analysis
  • Normal sets

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