The Gomory-Chvátal Closure of a Nonrational Polytope Is a Rational Polytope

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Gomory-Chvátal Closure of a Non-Rational Polytope is a Rational Polytope

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print ...

متن کامل

The Chvátal-Gomory Closure of an Ellipsoid Is a Polyhedron

It is well-know that the Chvátal-Gomory (CG) closure of a rational polyhedron is a rational polyhedron. In this paper, we show that the CG closure of a bounded full-dimensional ellipsoid, described by rational data, is a rational polytope. To the best of our knowledge, this is the first extension of the polyhedrality of the CG closure to a nonpolyhedral set. A key feature of the proof is to ver...

متن کامل

On the Chvátal-Gomory Closure of a Compact Convex Set

In this paper, we show that the Chvátal-Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver [17] for irrational polytopes1, and generalizes the same result for the case of rational polytopes [17], rational ellipsoids [8] and strictly convex bodies [7].

متن کامل

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...

متن کامل

Deciding 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics of Operations Research

سال: 2013

ISSN: 0364-765X,1526-5471

DOI: 10.1287/moor.1120.0565