Home > Research > Publications & Outputs > On a hierarchy of polytopes for integer quadrat...

Research

Associated organisational unit

Electronic data

  • miqpbits_ods25_REV

    Rights statement: 12m

    Accepted author manuscript, 329 KB, PDF document

    Embargo ends: 1/01/50

Keywords

View graph of relations

On a hierarchy of polytopes for integer quadratic programming

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

Forthcoming

Standard

On a hierarchy of polytopes for integer quadratic programming. / Galli, Laura; Letchford, Adam.
Mathematics, Algorithms and the Art and Science of Decision-Making. ed. / Michele Barbato; Nicola Bianchessi; Alberto Boggio Tomasaz. Springer, 2025.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

Harvard

Galli, L & Letchford, A 2025, On a hierarchy of polytopes for integer quadratic programming. in M Barbato, N Bianchessi & A Boggio Tomasaz (eds), Mathematics, Algorithms and the Art and Science of Decision-Making. Springer.

APA

Galli, L., & Letchford, A. (in press). On a hierarchy of polytopes for integer quadratic programming. In M. Barbato, N. Bianchessi, & A. Boggio Tomasaz (Eds.), Mathematics, Algorithms and the Art and Science of Decision-Making Springer.

Vancouver

Galli L, Letchford A. On a hierarchy of polytopes for integer quadratic programming. In Barbato M, Bianchessi N, Boggio Tomasaz A, editors, Mathematics, Algorithms and the Art and Science of Decision-Making. Springer. 2025

Author

Galli, Laura ; Letchford, Adam. / On a hierarchy of polytopes for integer quadratic programming. Mathematics, Algorithms and the Art and Science of Decision-Making. editor / Michele Barbato ; Nicola Bianchessi ; Alberto Boggio Tomasaz. Springer, 2025.

Bibtex

@inbook{17bb818c0a2d4b379fa0307d93792596,
title = "On a hierarchy of polytopes for integer quadratic programming",
abstract = "A folklore result in integer programming is that bounded integer variables can be replaced with binary variables, using bit representation. Under certain conditions, this can be used to reformulate mixed-integer quadratic programs as mixed-integer linear programs, and thereby render them easier to solve. In fact, several reformulation strategies can be found in the literature. We conduct a systematic comparison of these strategies by focusing on integer quadratic programs with box constraints, and present a hierarchy for the associated polytopes.",
keywords = "mixed-integer nonlinear programming, global optimisation",
author = "Laura Galli and Adam Letchford",
year = "2025",
month = may,
day = "8",
language = "English",
editor = "Michele Barbato and { Bianchessi}, Nicola and {Boggio Tomasaz}, Alberto",
booktitle = "Mathematics, Algorithms and the Art and Science of Decision-Making",
publisher = "Springer",

}

RIS

TY - CHAP

T1 - On a hierarchy of polytopes for integer quadratic programming

AU - Galli, Laura

AU - Letchford, Adam

PY - 2025/5/8

Y1 - 2025/5/8

N2 - A folklore result in integer programming is that bounded integer variables can be replaced with binary variables, using bit representation. Under certain conditions, this can be used to reformulate mixed-integer quadratic programs as mixed-integer linear programs, and thereby render them easier to solve. In fact, several reformulation strategies can be found in the literature. We conduct a systematic comparison of these strategies by focusing on integer quadratic programs with box constraints, and present a hierarchy for the associated polytopes.

AB - A folklore result in integer programming is that bounded integer variables can be replaced with binary variables, using bit representation. Under certain conditions, this can be used to reformulate mixed-integer quadratic programs as mixed-integer linear programs, and thereby render them easier to solve. In fact, several reformulation strategies can be found in the literature. We conduct a systematic comparison of these strategies by focusing on integer quadratic programs with box constraints, and present a hierarchy for the associated polytopes.

KW - mixed-integer nonlinear programming

KW - global optimisation

M3 - Chapter (peer-reviewed)

BT - Mathematics, Algorithms and the Art and Science of Decision-Making

A2 - Barbato, Michele

A2 - Bianchessi, Nicola

A2 - Boggio Tomasaz, Alberto

PB - Springer

ER -