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Bibliographic Details
Main Authors: Hosseinian, Seyedmohammadhossein, Schaefer, Andrew J.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.07117
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author Hosseinian, Seyedmohammadhossein
Schaefer, Andrew J.
author_facet Hosseinian, Seyedmohammadhossein
Schaefer, Andrew J.
contents An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those constraints can be obtained if the irrational parameters are polynomials of roots of integers over the field of rational numbers, leading to an equivalent rational formulation. We also establish a weaker result for IPs involving the general class of algebraic irrational parameters, which extends to IPs with a particular form of transcendental numbers.
format Preprint
id arxiv_https___arxiv_org_abs_2402_07117
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On Integer Programs with Irrational Data
Hosseinian, Seyedmohammadhossein
Schaefer, Andrew J.
Optimization and Control
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those constraints can be obtained if the irrational parameters are polynomials of roots of integers over the field of rational numbers, leading to an equivalent rational formulation. We also establish a weaker result for IPs involving the general class of algebraic irrational parameters, which extends to IPs with a particular form of transcendental numbers.
title On Integer Programs with Irrational Data
topic Optimization and Control
url https://arxiv.org/abs/2402.07117