QPLIB

A Library of Quadratic Programming Instances

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This website hosts a collection of problem instances from the diverse class of quadratic programming problems. Starting from 8,164 submitted instances, the final version of QPLIB contains 319 discrete and 134 continuous instances of different characteristics. For details on the library see the article

Fabio Furini, Emiliano Traversi, Pietro Belotti, Antonio Frangioni, Ambros Gleixner, Nick Gould, Leo Liberti, Andrea Lodi, Ruth Misener, Hans Mittelmann, Nikolaos Sahinidis, Stefan Vigerske, and Angelika Wiegele. QPLIB: A Library of Quadratic Programming Instances, Mathematical Programming Computation, 2018, DOI:10.1007/s12532-018-0147-4

and the statistics and documentation pages on this website. When using QPLIB, please cite the article above. The BibTeX entry is here.

History and updates

August, 20, 2024: Added solution points for instances QPLIB_2650, QPLIB_3814, and QPLIB_8500. Solution were found by KNITRO and contributed by Çağrı Latifoğlu.
July, 26, 2024: Updated solution point for instance QPLIB_9008. Improved solution was found by MOSEK and contributed by Çağrı Latifoğlu.
April, 23, 2024: Updated solution points for instances QPLIB_2036 and QPLIB_2096. Improved solutions were found by LS-IQCQP and contributed by Xiang He and Shaowei Cai.
February, 22, 2023: Updated solution points for instances QPLIB_3693 and QPLIB_3850. Improved solutions were found by QUBOWL and contributed by Daniel Rehfeldt.
August, 30, 2021: QPLIB is now licensed under CC-BY 4.0.
December 2, 2019: Added or updated solution points for instances QPLIB_{0698, 2168, 2205, 2626, 2703, 2707, 2823, 2880, 3105, 3177, 3347, 3510, 3524, 3525, 3533, 3580, 3605, 3625, 3631, 3650, 3729, 3780, 3850, 3859, 3913, 5527, 5573, 5721, 5925, 5926, 5927, 6597, 8547, 8595, 8758, 9008, 10007, 10016, 10020, 10021, 10032, 10036}.
September 22, 2018: Refereed article published online in Mathematical Programming Computation.
May 24, 2018: Fixed non-default variable types in .qplib version of some instances. For instances with a majority of integer variables, the variable type for the remaining continuous variables was wrong.
February 15, 2018: Added new instances QPLIB_{8500, 8547, 8553, 8585, 8595, 8683, 8758, 8784, 8803, 8810, 8815, 9008, 10001, 10002, 10003, 10004, 10005, 10006, 10007, 10008, 10009, 10010, 10011, 10012, 10013, 10014, 10015, 10016, 10017, 10018, 10019, 10020, 10021, 10022, 10023, 10024, 10025, 10026, 10027, 10028, 10029, 10030, 10031, 10032, 10033, 10034, 10035, 10036, 10037, 10038, 10039, 10040, 10041, 10042, 10043, 10044, 10045, 10046, 10047, 10048, 10049, 10050, 10051, 10052, 10053, 10054, 10055, 10056, 10057, 10058, 10059, 10060, 10061, 10062, 10063, 10064, 10065, 10066, 10067, 10068, 10069, 10070, 10071, 10072, 10073, 10074}.
October 26, 2017: Added feasible solution points obtained by running a variety of solvers with a 12 hour time limit. All solutions satisfy integrality requirements and variable bounds exactly; absolute constraint violations should be 1e-9 or less.
July 27, 2017: Fixed errors in the .qplib formatted versions of instances with quadratic constraints.
May 5, 2017: Tightening the tolerance for zero eigenvalues lead to changes in convexity information for instances QPLIB_{2635,2881,9030}.
May 4, 2017: Corrected convexity information for instances QPLIB_{2696,3049,3326,3554,3790,9048}.
February 15, 2017: New instance file formats online: AMPL's .mod and our newly developed .qplib.
February 6, 2017: The finalized instance selection for QPLIB 2014 goes online.
July 19, 2015: A first beta version containing 410 discrete instances and 138 continuous instances is online.
July 17, 2015: Emiliano Traversi presents on the collection and initial filtering of QPLIB instances at ISMP 2015 in Pittsburgh (slides).
January 21, 2014: First call for instances is out on dmanet. Until 2015, 8,164 instances are submitted.

Committee

The following researchers have been involved in the creation of QPLIB:

Pietro Belotti, Department of Electronics, Information and Bioengineering, Politecnico di Milano
Antonio Frangioni, Dipartimento di Informatica, Università di Pisa
Fabio Furini, DIAG, Sapienza University of Rome
Ambros Gleixner, HTW Berlin and Zuse Institute Berlin
Nick Gould, STFC-Rutherford Appleton Laboratory
Leo Liberti, CNRS LIX, Ecole Polytechnique
Andrea Lodi, Cornell Tech
Ruth Misener, Department of Computing, Imperial College London
Hans Mittelmann, School of Mathematical and Statistical Sciences, Arizona State University
Nikolaos Sahinidis, School of Chemical and Biomolecular Engineering, Georgia Institute of Technology
Emiliano Traversi, University of Montpellier
Stefan Vigerske, GAMS Software GmbH
Angelika Wiegele, Institut für Mathematik, Alpen-Adria-Universität Klagenfurt

We want to thank the Gaspard Monge Program for Optimization and Operations Research (PGMO) and GAMS for their support of the QPLIB project.

Contact

For questions and comments please contact the main coordinators Fabio Furini and Emiliano Traversi. Regarding the website or for updating best-known solutions, contact Stefan Vigerske.