- The integer hull of a convex rational polytope Jean B. Lasserre (lasserrelaas.fr) Abstract: Given $A\in Z^{m\times n}$ and $b\in Z^m$, we consider the integer program $\max \{c'x\vert Ax=b;x\in N^n\}$ and provide an equivalent and explicit linear program $\max \{\widehat{c}'q\vert M q=r;q\geq 0\}$, where $M,r,\widehat{c}$ are easily obtained from $A,b,c$ with no calculation. We also provide an explicit algebraic characterization of the integer hull of the convex polytope $P=\{x\in\R^n\vert Ax=b;x\geq0\}$. All strong valid inequalities can be obtained from the generators of a convex cone whose definition is explicit in terms of $M$. Keywords: Integer programming; convex polytope; integer hull Category 1: Integer Programming Category 2: Combinatorial Optimization (Polyhedra ) Citation: Technical report #03018, LAAS, Toulouse, January 2003. Discr. Comput. Geom. 32 (2004), 129--139 Download: Entry Submitted: 04/26/2003Entry Accepted: 04/26/2003Entry Last Modified: 05/19/2004Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.