Subset Algebra Lift Operators for 0-1 Integer Programming

Authors:
Daniel Bienstock;Mark Zuckerberg
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
2005

Citing 0
Cited 10

Computation of the Lasserre Ranks of Some Polytopes

Mathematics of Operations Research
Unification of lower-bound analyses of the lift-and-project rank of combinatorial optimization polyhedra

Discrete Applied Mathematics
A p-cone sequential relaxation procedure for 0-1 integer programs

Optimization Methods & Software - GLOBAL OPTIMIZATION
Complexity analyses of Bienstock-Zuckerberg and lasserre relaxations on the matching and stable set polytopes

IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Eigenvalue techniques for convex objective, nonconvex optimization problems

IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Approximate formulations for 0-1 knapsack sets

Operations Research Letters
Note: On the polyhedral lift-and-project methods and the fractional stable set polytope

Discrete Optimization
Tree-width and the Sherali-Adams operator

Discrete Optimization
A new necessary and sufficient global optimality condition for canonical DC problems

Journal of Global Optimization
Lifts of Convex Sets and Cone Factorizations

Mathematics of Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

We extend the Sherali--Adams, Lovász--Schrijver, Balas--Ceria--Cornuéjols, and Lasserre lift-and-project methods for 0-1 optimization by considering liftings to subset algebras. Our methods yield polynomial-time algorithms for solving a relaxation of a set-covering problem at least as strong as that given by the set of all valid inequalities with small coefficients and, more generally, all valid inequalities where the right-hand side is not very large relative to the positive coefficients in the left-hand side. Applied to generalizations of vertex-packing problems, our methods yield, in polynomial time, relaxations that have unbounded rank using, for example, the N+ operator.