
Lifting Linear Extension Complexity Bounds to the MixedInteger Setting
Mixedinteger mathematical programs are among the most commonly used mod...
read it

Parity Polytopes and Binarization
We consider generalizations of parity polytopes whose variables, in addi...
read it

Tight MIP formulations for bounded length cyclic sequences
We study cyclic binary strings with bounds on the lengths of the interva...
read it

An improved binary programming formulation for the secure domination problem
The secure domination problem, a variation of the domination problem wit...
read it

Extended formulations from communication protocols in outputefficient time
Deterministic protocols are wellknown tools to obtain extended formulat...
read it

Separable and transitive graphoids
We examine three probabilistic formulations of the sentence a and b are ...
read it

Extended formulations for matroid polytopes through randomized protocols
Let P be a polytope. The hitting number of P is the smallest size of a h...
read it
Binary extended formulations and sequential convexification
A binarization of a bounded variable x is a linear formulation with variables x and additional binary variables y_1,…, y_k, so that integrality of x is implied by the integrality of y_1,…, y_k. A binary extended formulation of a polyhedron P is obtained by adding to the original description of P binarizations of some of its variables. In the context of mixedinteger programming, imposing integrality on 0/1 variables rather than on general integer variables has interesting convergence properties and has been studied both from the theoretical and from the practical point of view. We propose a notion of natural binarizations and binary extended formulations, encompassing all the ones studied in the literature. We give a simple characterization of the vertices of such formulations, which allows us to study their behavior with respect to sequential convexification. disjunctions. In particular, given a binary extended formulation and binarization B of one of its variables x, we study a parameter that measures the progress made towards ensuring the integrality of x via application of sequential convexification. We formulate this parameter, which we call rank, as the solution of a set covering problem and express it exactly for the classical binarizations from the literature.
READ FULL TEXT
Comments
There are no comments yet.