## Solving lift-and-project relaxations of binary integer programs

Venue: | SIAM Journal on Optimization |

Citations: | 22 - 2 self |

### BibTeX

@ARTICLE{Burer_solvinglift-and-project,

author = {Samuel Burer and Dieter Vandenbussche},

title = {Solving lift-and-project relaxations of binary integer programs},

journal = {SIAM Journal on Optimization},

year = {},

volume = {16},

pages = {726--750}

}

### OpenURL

### Abstract

Abstract. 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.