Year: 2026
Type: article
Abstract: An integer program (IP) with a finite number of feasible solutions may have an unbounded continuous relaxation if it contains irrational parameters, due to implicit constraints induced by those irrational numbers. For IPs with polynomial constraints, we show that these implicit constraints can be derived explicitly when the irrational parameters belong to an extension field of the rational numbers by roots of integers, leading to a rational reformulation. We also present a weaker result for IPs involving the broader class of algebraic irrational numbers, which extends to IPs containing a particular form of transcendental numbers.
Source: Mathematical Programming
Institutions: North Carolina State University, Rice University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Office of Naval Research
Award: G954065927
OpenAlex ID: W4391800762