TY - JOUR A1 - Bonami, Pierre T1 - On optimizing over lift-and-project closures T2 - Mathematical Programming Computation N2 - The strengthened lift-and-project closure of a mixed integer linear pro- gram is the polyhedron obtained by intersecting all strengthened lift-and-project cuts obtained from its initial formulation, or equivalently all mixed integer Gomory cuts read from all tableaux corresponding to feasible and infeasible bases of the LP relax- ation. In this paper, we present an algorithm for approximately optimizing over the strengthened lift-and-project closure. The originality of our method is that it relies on a cut generation linear programming problem which is obtained from the original LP relaxation by only modifying the bounds on the variables and constraints. This separation LP can also be seen as dual to the cut generation LP used in disjunc- tive programming procedures with a particular normalization. We study properties of this separation LP, and discuss how to use it to approximately optimize over the strengthened lift-and-project closure. Finally, we present computational experiments and comparisons with recent related works. KW - Software KW - Theoretical Computer Science Y1 - 2012 UR - https://opus4.kobv.de/opus4-mpc/frontdoor/index/index/docId/39 SN - 1867-2949 VL - 4 IS - 2 SP - 151 EP - 179 PB - Springer Science and Business Media LLC ER -