Approximating the Split Closure
نویسندگان
چکیده
منابع مشابه
Approximating the Split Closure
The split closure has been proved in practice to be a very tight approximation of the integer hull formulation of a generic mixed-integer linear program. However, exact separation procedures for optimizing over the split closure have unacceptable computing times in practice, hence many different heuristic strategies have been proposed in the last years. In this paper we present a new overall fr...
متن کاملOptimizing over the split closure
The polyhedron defined by all the split cuts obtainable directly (i.e. without iterated cut generation) from the LP-relaxation P of a mixed integer program (MIP) is termed the (elementary, or rank 1) split closure of P . This paper deals with the problem of optimizing over the split closure. This is accomplished by repeatedly solving the following separation problem: given a fractional point, s...
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In the seventies, Balas introduced intersection cuts for a Mixed Integer Linear Program (MILP), and showed that these cuts can be obtained by a closed form formula from a basis of the standard linear programming relaxation. In the early nineties, Cook, Kannan and Schrijver introduced the split closure of an MILP, and showed that the split closure is a polyhedron. In this paper, we show that the...
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Split cuts form a well-known class of valid inequalities for mixed-integer programming problems (MIP). Cook et al. (1990) showed that the split closure of a rational polyhedron P is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We also show how this result can be used to prove that some generaliz...
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Boolean affine relations, which combine affine inequalities by boolean connectives are ubiquitous in all kind of static program analyzes. One of the crucial operations on such relations is transitive closure, which is closely related to the construction of loop inductive invariants. I present here a new over-approximation algorithm, which has the interesting property of being extendible for inc...
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ژورنال
عنوان ژورنال: INFORMS Journal on Computing
سال: 2013
ISSN: 1091-9856,1526-5528
DOI: 10.1287/ijoc.1120.0543