On the connection of the Sherali-Adams closure and border bases

The Sherali-Adams lift-and-project hierarchy is a fundamental construct in integer programming, which provides successively tighter linear programming relaxations of the integer hull of a polytope. We initiate a new approach to understanding the Sherali-Adams procedure by relating it to methods from computational algebraic geometry. Our main result is a refinement of the Sherali-Adams procedure that … Read more