On the Intersection of Two Particular Convex Sets

Xiaoqi Yang, C. J. Goh

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

In this note, necessary and sufficient conditions are given for the intersection of the m-1 simplex co{ξ1, . . . , ξm} of m affinely independent vectors ξ1, . . . , ξmof ℝnand the negative orthant ℝn-to be empty, i.e., co{ξ1, . . . , ξm} ∩ ℝn-= ∅, where m ≤ n. It is also shown that the special case m=2 can be checked easily. These results suggest that the above-mentioned emptiness can be checked recursively. Some numerical examples are given to illustrate the results. Potential applications of these results include the compatible multicommodity flow problems and satisficing solution problems.
Original languageEnglish
Pages (from-to)483-491
Number of pages9
JournalJournal of Optimization Theory and Applications
Volume89
Issue number2
DOIs
Publication statusPublished - 1 Jan 1996
Externally publishedYes

Keywords

  • Convex programs
  • Convex sets
  • Simplexes

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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