Some properties of the Boolean Quadric Polytope
نویسندگان
چکیده
The topic of our research is unconstrained 0-1 quadratic programming. We find some properties of the Boolean Quadric Polytope, which is obtained from the standard linearization of the given 0-1 quadratic function. By using a result obtained by Deza and Laurent on a class of hypermetric inequalities for the Cut Polytope, we find a necessary and sufficient condition for a class of inequalities to be facet defining for the Boolean Quadric Polytope. Furthermore we find a property characterizing the non integral vertices of a class of relaxations of the Boolean Quadric Polytope.
منابع مشابه
Some Characteristics of the Simple Boolean Quadric Polytope Extension
Following the seminal work of Padberg on the Boolean quadric polytope BQP and its LP relaxation BQPLP , we consider a natural extension: SATP and SATPLP polytopes, with BQPLP being projection of the SATPLP face (and BQP projection of the SATP face). We consider the problem of integer recognition: determine whether the maximum of a linear objective function is achieved at an integral vertex of a...
متن کاملOn the strength of the cycle relaxation for the boolean quadric polytope
We study unconstrained zero-one quadratic programming problems. The boolean quadric polytope arises from a standard linearization of the objective function and has been extensively studied in the literature. A well-known relaxation of the boolean quadric polytope is the cycle relaxation, which is closely related to the metric polytope for max-cut. We characterize the sign patterns of the object...
متن کاملMaximum-Entropy Sampling and the Boolean Quadric Polytope
We consider a bound for the maximum-entropy sampling problem (MESP) that is based on solving a max-det problem over a relaxation of the Boolean Quadric Polytope (BQP). This approach to MESP was first suggested by Christoph Helmberg over 15 years ago, but has apparently never been further elaborated or computationally investigated. We find that the use of a relaxation of BQP that imposes semidef...
متن کاملThe volume of relaxed Boolean-quadric and cut polytopes
For n 2, the boolean quadric polytope P n is the convex hull in d := ? n+1 2 dimensions of the binary solutions of x i x j = y ij , for all i < j in N := f1; 2; :::; ng. The polytope is naturally modeled by a somewhat larger polytope; namely, Q n the solution set of y ij x i , y ij x j , x i + x j 1 + y ij , y ij 0, for all i; j in N. In a rst step toward seeing how well Q n approximates P n , ...
متن کاملConstruction de facettes pour le polytope du sac-à-dos quadratique en 0-1
We build facets of the quadratic 0-1 knapsack polytope following two different approaches. The quadratic 0-1 knapsack polytope is included in the Boolean quadric polytope introduced by Padberg [12] for unconstrained 0-1 quadratic problem. So in a first approach, we ask the question which are the facets of the Boolean quadric polytope that are still facets of the quadratic 0-1 knapsack polytope....
متن کامل