ISSN:
1573-2878
Schlagwort(e):
Simplexes
;
convex sets
;
convex programs
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract In this note, necessary and sufficient conditions are given for the intersection of them−1 simplex co {ξ1,...,ξ m } ofm affinely independent vectors ξ1,...,ξ m of ℝ n and the negative orthant ℝ − n to be empty, i.e., $$co\{ \xi ^1 ,...,\xi ^m \} \cap \mathbb{R}_ - ^n = \emptyset ,$$ wherem≤n. It is also shown that the special casem=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.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF02192542
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