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 |
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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
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.
In: Mathematical Programming Computation, Vol. 11, No. 2, 01.06.2019, p. 237-265.Research output: Contribution to journal › Article
}
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
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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 -