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 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.

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  1. Chen, Tong; Lasserre, Jean-Bernard; Magron, Victor; Pauwels, Edouard: A sublevel moment-SOS hierarchy for polynomial optimization (2022)
  2. Hribar, Rok; Hrga, Timotej; Papa, Gregor; Petelin, Gašper; Povh, Janez; Pržulj, Nataša; Vukašinović, Vida: Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem (2022)
  3. Adjé, Assalé: Quadratic maximization of reachable values of affine systems with diagonalizable matrix (2021)
  4. Bergman, David; Lozano, Leonardo: Decision diagram decomposition for quadratically constrained binary optimization (2021)
  5. Edirisinghe, Chanaka; Jeong, Jaehwan; Chen, Jingnan: Optimal portfolio deleveraging under market impact and margin restrictions (2021)
  6. Gleixner, Ambros; Hendel, Gregor; Gamrath, Gerald; Achterberg, Tobias; Bastubbe, Michael; Berthold, Timo; Christophel, Philipp; Jarck, Kati; Koch, Thorsten; Linderoth, Jeff; Lübbecke, Marco; Mittelmann, Hans D.; Ozyurt, Derya; Ralphs, Ted K.; Salvagnin, Domenico; Shinano, Yuji: MIPLIB 2017: data-driven compilation of the 6th mixed-integer programming library (2021)
  7. Liuzzi, G.; Locatelli, M.; Piccialli, V.; Rass, S.: Computing mixed strategies equilibria in presence of switching costs by the solution of nonconvex QP problems (2021)
  8. Bettiol, Enrico; Létocart, Lucas; Rinaldi, Francesco; Traversi, Emiliano: A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs (2020)
  9. Madani, Ramtin; Kheirandishfard, Mohsen; Lavaei, Javad; Atamtürk, Alper: Penalized semidefinite programming for quadratically-constrained quadratic optimization (2020)
  10. Mittelmann, Hans D.: Benchmarking optimization software -- a (Hi)story (2020)
  11. Aldasoro, Unai; Merino, María; Pérez, Gloria: Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic (2019)
  12. 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: QPLIB: a library of quadratic programming instances (2019)
  13. Montanher, Tiago; Neumaier, Arnold; Domes, Ferenc: A computational study of global optimization solvers on two trust region subproblems (2018)