### Abstract

This paper describes a new instance library for quadratic programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function and/or the constraints are quadratic. QP is a very diverse class of problems, comprising sub-classes ranging from trivial to undecidable. This diversity is reflected in the variety of QP solution methods, ranging from entirely combinatorial approaches to completely continuous algorithms, including many methods for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the different, interested communities is therefore important. We propose a simple taxonomy for QP instances leading to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.

Original language | English (US) |
---|---|

Pages (from-to) | 237-265 |

Number of pages | 29 |

Journal | Mathematical Programming Computation |

Volume | 11 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2019 |

### Fingerprint

### Keywords

- Binary quadratic programming
- Instance library
- Mixed-Integer Quadratically Constrained Quadratic Programming
- Quadratic programming

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software

### Cite this

*Mathematical Programming Computation*,

*11*(2), 237-265. https://doi.org/10.1007/s12532-018-0147-4

**QPLIB : a library of quadratic programming instances.** / Furini, Fabio; Traversi, Emiliano; Belotti, Pietro; Frangioni, Antonio; Gleixner, Ambros; Gould, Nick; Liberti, Leo; Lodi, Andrea; Misener, Ruth; Mittelmann, Hans; Sahinidis, Nikolaos V.; Vigerske, Stefan; Wiegele, Angelika.

Research output: Contribution to journal › Article

*Mathematical Programming Computation*, vol. 11, no. 2, pp. 237-265. https://doi.org/10.1007/s12532-018-0147-4

}

TY - JOUR

T1 - QPLIB

T2 - a library of quadratic programming instances

AU - Furini, Fabio

AU - Traversi, Emiliano

AU - Belotti, Pietro

AU - Frangioni, Antonio

AU - Gleixner, Ambros

AU - Gould, Nick

AU - Liberti, Leo

AU - Lodi, Andrea

AU - Misener, Ruth

AU - Mittelmann, Hans

AU - Sahinidis, Nikolaos V.

AU - Vigerske, Stefan

AU - Wiegele, Angelika

PY - 2019/6/1

Y1 - 2019/6/1

N2 - This paper describes a new instance library for quadratic programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function and/or the constraints are quadratic. QP is a very diverse class of problems, comprising sub-classes ranging from trivial to undecidable. This diversity is reflected in the variety of QP solution methods, ranging from entirely combinatorial approaches to completely continuous algorithms, including many methods for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the different, interested communities is therefore important. We propose a simple taxonomy for QP instances leading to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.

AB - This paper describes a new instance library for quadratic programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function and/or the constraints are quadratic. QP is a very diverse class of problems, comprising sub-classes ranging from trivial to undecidable. This diversity is reflected in the variety of QP solution methods, ranging from entirely combinatorial approaches to completely continuous algorithms, including many methods for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the different, interested communities is therefore important. We propose a simple taxonomy for QP instances leading to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.

KW - Binary quadratic programming

KW - Instance library

KW - Mixed-Integer Quadratically Constrained Quadratic Programming

KW - Quadratic programming

UR - http://www.scopus.com/inward/record.url?scp=85065230079&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065230079&partnerID=8YFLogxK

U2 - 10.1007/s12532-018-0147-4

DO - 10.1007/s12532-018-0147-4

M3 - Article

VL - 11

SP - 237

EP - 265

JO - Mathematical Programming Computation

JF - Mathematical Programming Computation

SN - 1867-2949

IS - 2

ER -