Aardal, Karen
**
Wolsey, Laurence
[UCL]
**
We study different extended formulations for the set X = {x [belong] Z exp.n | Ax = Ax exp.0} in order to tackle the feasibility problem for the set X+ = X [intersection] Z+ exp.n . Here the goal is not to find an improved polyhedral relaxation of conv(X+), but rather to reformulate in such a way that the new variables introduced provide good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. For the case that A has one row a we analyze the reformulations in more detail. In particular, we determine the integer width of the extended formulations in the direction of the last coordinate, and derive a lower bound on the Frobenius number of a. We also suggest how a decomposition of the vector a can be obtained that will provide a useful extended formulation. Our theoretical results are accompanied by a small computational study.

Bibliographic reference |
Aardal, Karen ; Wolsey, Laurence. *Lattice based extended formulations for integer linear equality systems.* CORE Discussion Papers ; 2007/17 (2007) |

Permanent URL |
http://hdl.handle.net/2078.1/5103 |