1. ON THE CONVERGENCE OF THE AFFINE HULL OF THE CHVÁTAL GOMORY CLOSURES.
- Author
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AVERKOV, GENNADIY, CONFORTI, MICHELE, DEL PIA, ALBERTO, DI SUMMA, MARCO, and FAENZA, YURI
- Subjects
- *
POLYHEDRA , *INTEGERS , *ITERATIVE methods (Mathematics) , *CLOSURE operators , *OPERATOR theory - Abstract
Given an integral polyhedron P ⊆ ℝn and a rational polyhedron Q ⊆ ℝn containing the same integer points as P, we investigate how many iterations of the Chvatal--Gomory closure operator have to be performed on Q to obtain a polyhedron contained in the affine hull of P. We show that if P contains an integer point in its relative interior, then such a number of iterations can be bounded by a function depending only on n. On the other hand, we prove that if P is not full-dimensional and does not contain any integer point in its relative interior, then no finite bound on the number of iterations exists. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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