Conic positive definiteness and sharp minima of fractional orders in vector optimization problems

Xi Yin Zheng, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


Motivated by the fact that the usual positive definiteness does not work in an infinite space, we introduce the concept of S-positive definiteness with respect to an ordering cone in a general Banach space and show that the S-positive definiteness plays the same role as the usual positive definiteness in the finite dimensional case. As applications, we study sharp and weak sharp minima of fractional orders in vector optimization.
Original languageEnglish
Pages (from-to)619-629
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Jul 2012


  • Conic positive definiteness
  • Ideal solution
  • Pareto solution
  • Sharp minima
  • Weak Pareto solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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