The Geometry of Strict Maximality

Enrico Miglierina, E. Casini, E. Miglierina

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3 Citazioni (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.
Lingua originaleEnglish
pagine (da-a)3146-3160
Numero di pagine15
RivistaSIAM Journal on Optimization
Volume20
DOI
Stato di pubblicazionePubblicato - 2010

Keywords

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

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