QPLIB: a library of quadratic programming instances

  • Fabio FuriniEmail author
  • Emiliano Traversi
  • Pietro Belotti
  • Antonio Frangioni
  • Ambros Gleixner
  • Nick Gould
  • Leo Liberti
  • Andrea Lodi
  • Ruth Misener
  • Hans Mittelmann
  • Nikolaos V. Sahinidis
  • Stefan Vigerske
  • Angelika Wiegele
Full Length Paper


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.


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

Mathematics Subject Classification

90C06 90C25 



We are grateful to all the donors who provided instances for the library. We gratefully acknowledge the financial support of the Gaspard Monge Program for Optimization and operations research (PGMO) and the logistic support of GAMS for having provided us with a license for their software. Finally, we would like to acknowledge the financial and networking support by the COST Action TD1207. The work of the fifth and twelfth author was supported by the Research Campus MODAL Mathematical Optimization and Data Analysis Laboratories funded by the Federal Ministry of Education and Research (BMBF Grant 05M14ZAM). The work of the sixth author was supported by the EPSRC grant EP/M025179/1. All responsibility for the content of this publication is assumed by the authors.

Supplementary material

12532_2018_147_MOESM1_ESM.pdf (195 kb)
Supplementary material 1 (pdf 194 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and The Mathematical Programming Society 2018

Authors and Affiliations

  • Fabio Furini
    • 1
    Email author
  • Emiliano Traversi
    • 2
  • Pietro Belotti
    • 3
  • Antonio Frangioni
    • 4
  • Ambros Gleixner
    • 5
  • Nick Gould
    • 6
  • Leo Liberti
    • 7
  • Andrea Lodi
    • 8
  • Ruth Misener
    • 9
  • Hans Mittelmann
    • 10
  • Nikolaos V. Sahinidis
    • 11
  • Stefan Vigerske
    • 12
  • Angelika Wiegele
    • 13
  1. 1.LAMSADEUniversité Paris DauphineParisFrance
  2. 2.LIPNUniversité de Paris 13VilletaneuseFrance
  3. 3.Xpress-Optimizer TeamFICOBirminghamUK
  4. 4.Dipartimento di InformaticaUniversità di PisaPisaItaly
  5. 5.Department of Mathematical OptimizationZuse Institute BerlinBerlinGermany
  6. 6.STFC-Rutherford Appleton LaboratoryChiltonEngland
  7. 7.CNRS LIXÉcole PolytechniquePalaiseauFrance
  8. 8.CERC, École Polytechnique de MontrealMontrealCanada
  9. 9.Department of ComputingImperial College LondonLondonUK
  10. 10.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA
  11. 11.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA
  12. 12.GAMS Software GmbHc/o Zuse Institute BerlinBerlinGermany
  13. 13.Institut für MathematikAlpen-Adria-Universität KlagenfurtKlagenfurt am WörtherseeAustria

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