The Geometry of Strict Maximality

Enrico Miglierina, E. Casini, E. Miglierina

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The notion of a strictly maximal point is a concept of proper maximality that plays an important role in the study of the stability of vector optimization problems. The aim of this paper is to study some properties of this notion with particular attention to geometrical aspects. More precisely, we individuate some relationships between strict maximality and the properties of the bases of the ordering cone. In order to prove this result, a new characterization of the existence of a bounded base for a closed convex cone is given. Moreover, we link strict maximality to the geometrical notion of strongly exposed points of a given set. Finally, we deal with the linear scalarization for the strictly maximal points.
Original languageEnglish
Pages (from-to)3146-3160
Number of pages15
JournalSIAM Journal on Optimization
Volume20
DOIs
Publication statusPublished - 2010

Keywords

  • base for a cone
  • linear scalarization
  • proper maximality
  • strict maximality
  • vector optimization

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