Revival of the Gomory cuts in the 1990's
نویسنده
چکیده
منابع مشابه
The Chvátal-Gomory Closure of a Strictly Convex Body
Chv́atal-Gomory (CG) cuts are one of the first classes of cutting planes presented in the literature [14]. They have been at the heart of various fundamental theoretical and computational breakthroughs in IP. For example, Gomory [14] introduced CG cuts to present the first finite cutting plane algorithm for bounded IP problems. CG cuts can be used to obtain the convex hull of integer feasible so...
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In this thesis, we examine theoretical aspects of the Gomory-Chvital closure of polyhedra. A Gomory-Chvital cutting plane for a polyhedron P is derived from any rational inequality that is valid for P by shifting the boundary of the associated half-space towards the polyhedron until it intersects an integer point. The Gomory-ChvAital closure of P is the intersection of all half-spaces defined b...
متن کاملDeciding Emptiness of the Gomory-Chvátal Closure is NP-Complete, Even for a Rational Polyhedron Containing No Integer Point
Gomory-Chvátal cuts are prominent in integer programming. The Gomory-Chvátal closure of a polyhedron is the intersection of all half spaces defined by its Gomory-Chvátal cuts. In this paper, we show that it is NP-complete to decide whether the Gomory-Chvátal closure of a rational polyhedron is empty, even when this polyhedron contains no integer point. This implies that the problem of deciding ...
متن کاملStrengthening Chvátal-Gomory cuts and Gomory fractional cuts
Chvátal-Gomory and Gomory fractional cuts are well-known cutting planes for pure integer programming problems. Various methods for strengthening them are known, for example based on subadditive functions or disjunctive techniques. We present a new and surprisingly simple strengthening procedure, discuss its properties, and present some computational results.
متن کاملOn the membership problem for the {0, 1/2}-closure
In integer programming, {0, 1/2}-cuts are Gomory–Chvátal cuts that can be derived from the original linear system by using coefficients of value 0 or 1/2 only. The separation problem for {0, 1/2}-cuts is strongly NP-hard. We show that separation remains strongly NP-hard, even when all integer variables are binary. © 2011 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Annals OR
دوره 149 شماره
صفحات -
تاریخ انتشار 2007