Lifting operators for 0-1 integer programming (Daniel Bienstock)
This research extends the work of Lovasz and Schrijver, Sherali-Adams, and
Lasserre, on the idea of lifting an n-dimensional polyhedron to a space
whose coordinates are indexed by members of a subset-lattice of an n-element
Instead, in work to appear in the PhD dissertation of Mark Zuckerberg, we have devised operators that lift to a space whose coordinates are indexed by the much larger subset algebra of an n-element set.
This leads to provably stronger operators. As an example of our results, we have obtained a polynomial-time algorithm that solves a relaxation of set-covering problems that is stronger than that provided by the set of all valid inequalities with coefficients 0,1,2, ..., k (for any fixed k).
Our current research centers on extending these operators with the goal of
making them computationally practicable.