Solving Lift-and-Project Relaxations of Binary Integer Programs

We propose a method for optimizing the lift-and-project relaxations of binary integer programs introduced by Lovász and Schrijver. In particular, we study both linear and semidefinite relaxations. The key idea is a restructuring of the relaxations, which isolates the complicating constraints and allows for a Lagrangian approach. We detail an enhanced subgradient method and discuss its efficient implementation. Computational results illustrate that our algorithm produces tight bounds more quickly than state-of-the-art linear and semidefinite solvers.