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On the intersection of two particular convex sets (1996)

Yang, X. Q. ; Goh, C. J.

Springer

Journal of optimization theory and applications 89 (1996), S. 483-491

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ISSN: 1573-2878

Keywords: Simplexes ; convex sets ; convex programs

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02192542

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