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, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many 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 many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads 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.

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Author:Fabio Furini, Emiliano Traversi, Pietro Belotti, Antonio FrangioniORCiD, Ambros GleixnerORCiD, Nick Gould, Leo Liberti, Andrea LodiORCiD, Ruth Misener, Hans Mittelmann, Nikolaos V. Sahinidis, Stefan Vigerske, Angelika Wiegele
Document Type:Article
Parent Title (English):Mathematical Programming Computation
First Page:237
Last Page:265
Year of first publication:2019