Computing an Integer Point of a Class of Convex Sets

C. Dang

Journal of Optimization Theory and Applications, 2001, vol. 108, issue 2, No 6, 333-348

Abstract: Abstract A simplicial algorithm is proposed for computing an integer point of a convex set C⊂Rn satisfying $$x = \max \{ x^1 ,x^2 \} = (\max \{ _1^1 ,x_1^2 \} ,...,\max \{ x_n^1 ,x_n^2 \} ^T \in C,$$ with $$x^1 = (x_1^1 ,x_2^1 ,...,x_n^1 )^T \in C,{\text{ }}x^2 = (x_1^2 ,x_2^2 ,...,x_n^2 )^T \in C.$$ The algorithm subdivides R n into integer simplices and assigns an integer labelto each integer point of R n. Starting at an arbitraryinteger point, the algorithm follows a finite simplicial path that leads either to an integer point of C or to the conclusion that C has no integer point.

Keywords: integer points; integer labeling; triangulations; simplicial methods (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1026438301292

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