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 language | English |
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Pages (from-to) | 483-491 |
Number of pages | 9 |
Journal | Journal of Optimization Theory and Applications |
Volume | 89 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 1996 |
Externally published | Yes |
Keywords
- Convex programs
- Convex sets
- Simplexes
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics