QPLIB: a library of quadratic programming instances

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...

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Bibliographic Details
Published in:Mathematical programming computation 2019-06, Vol.11 (2), p.237-265
Main Authors: 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
Format: Article
Language:English
Subjects:
Algorithms
Combinatorial analysis
Full Length Paper
Libraries
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Quadratic programming
Solvers
Taxonomy
Theory of Computation
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Summary: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.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-018-0147-4