QPLIB: a library of quadratic programming instances

Fabio Furini, 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

Research output: Contribution to journalArticle

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)237-265
Number of pages29
JournalMathematical Programming Computation
Volume11
Issue number2
DOIs
StatePublished - Jun 1 2019

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Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software

Cite this

Furini, F., Traversi, E., Belotti, P., Frangioni, A., Gleixner, A., Gould, N., Liberti, L., Lodi, A., Misener, R., Mittelmann, H., Sahinidis, N. V., Vigerske, S., & Wiegele, A. (2019). QPLIB: a library of quadratic programming instances. Mathematical Programming Computation, 11(2), 237-265. https://doi.org/10.1007/s12532-018-0147-4