TY - JOUR A1 - Furini, Fabio A1 - Traversi, Emiliano A1 - Belotti, Pietro A1 - Frangioni, Antonio A1 - Gleixner, Ambros A1 - Gould, Nick A1 - Liberti, Leo A1 - Lodi, Andrea A1 - Misener, Ruth A1 - Mittelmann, Hans A1 - Sahinidis, Nikolaos V. A1 - Vigerske, Stefan A1 - Wiegele, Angelika T1 - QPLIB: A Library of Quadratic Programming Instances T2 - Mathematical Programming Computation 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, 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. Y1 - 2018 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6755 VL - 11 IS - 2 SP - 237 EP - 265 ER -