This paper is concerned with the application of semidefinite programming to the satisfiability problem, and in particular with using semidefinite liftings to efficiently obtain proofs of unsatisfiability. We focus on the Tseitin satisfiability instances which are known to be hard for many proof systems. We present an explicit semidefinite programming problem with dimension linear in … Read more
We describe an effective method for doing binary-encoded modeling, in the context of 0/1 linear programming, when the number of feasible configurations is not a power of two. Our motivation comes from modeling all-different restrictions. ArticleDownload View PDF
We propose a simple and sufficiently fast separation procedure to identify cover inequalities for the multidimensional knapsack problem. It is based on the solution of a conventional integer programming model. Solving this kind of integer programs are usually considered expensive and the proposed method may have been overlooked because of this assumption. The results of … Read more
We show that for any fixed rank, the closure of a set covering problem (and related problems) can be approximated in polynomial time — we can epsilon-approximate any linear program over the closure in polynomial time. CitationCORC report TR-2003-01, Computational Optimization Research Center, Columbia UniversityArticleDownload View PDF
We propose a method for optimizing the lift-and-project relaxations of binary integer programs introduced by Lov\’asz 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 … Read more
In this study, a lifting procedure is applied to some existing formulations of the Diameter Constrained Minimum Spanning Tree Problem. This problem typically models network design applications where all vertices must communicate with each other at minimum cost, while meeting or surpassing a given quality requirement. An alternative formulation is also proposed for instances of … Read more
We present a unifying framework to establish a lower-bound on the number of semidefinite programming based, lift-and-project iterations (rank) for computing the convex hull of the feasible solutions of various combinatorial optimization problems. This framework is based on the maps which are commutative with the lift-and-project operators. Some special commutative maps were originally observed by … Read more
We describe strong mixed-integer programming formulations for robust mixed 0-1 programming with uncertainty in the objective coefficients. In particular, we focus on an objective uncertainty set described as a polytope with a budget constraint. We show that for a robust 0-1 problem, there is a tight linear programming formulation with size polynomial in the size … Read more
Interior-point methods (IPMs), originally conceived in the context of linear programming have found a variety of applications in integer programming, and combinatorial optimization. This survey presents an up to date account of IPMs in solving NP-hard combinatorial optimization problems to optimality, and also in developing approximation algorithms for some of them. The surveyed approaches include … Read more
In the context of integer programming, we develop a polyhedral method for linearizing a product of a pair of real linear functions in 0/1 variables. As an example, by writing a pair of integer variables in binary expansion, we have a technique for linearizing their product. We give a complete linear description for the resulting … Read more