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QPLIB: a library of quadratic programming instances

Fabio Furini, Emiliano Traversi, Pietro Belotti, Antonio Frangioni, Ambros Gleixner, Nick Gould, Leo Liberti, Andrea Lodi, Ruth Misener, Hans Mittelmann, Nikolaos V. Sahinidis, Stefan Vigerske (+1 others)
2018 Mathematical Programming Computation  
, and nonconvex quadratic constraints of QPLIB instances.  ...  Conclusions This manuscript describes the first comprehensive library of instances for Quadratic Programming (QP).  ...  Any blank lines, or lines starting with any of the characters !, % or # are ignored. Each term in the first column of Table 8 denotes a required value.  ... 
doi:10.1007/s12532-018-0147-4 fatcat:7q7dunjewffb3ca2am6kmuf4im

MIPLIBing: Seamless Benchmarking of Mathematical Optimization Problems and Metadata Extensions

Thiago Serra, Ryan J. O'Neil
2020 SN Operations Research Forum  
Public libraries of problems such as Mixed Integer Programming Library (MIPLIB) are fundamental to creating a common benchmark for measuring algorithmic advances across mathematical optimization solvers  ...  In particular, we present MIPLIBing: a Python library that automatically downloads queried subsets from the current versions of MIPLIB, MINLPLib, and QPLIB, provides a centralized local cache across projects  ...  Acknowledgments We thank the anonymous reviewers for their feedback and suggestion to improve this manuscript and expand the scope of MIPLIBing.  ... 
doi:10.1007/s43069-020-00024-1 fatcat:63wsovz5hjbttmetajihqibkam

Benchmarking Optimization Software - a (Hi)Story

Hans D. Mittelmann
2020 SN Operations Research Forum  
In late 2018, an event had a major impact (the "story") on this service which had gained considerable notoriety.  ...  In the mean time, another major problem library had been published, QPLIB [28] . At INFORMS 2018, we had already three parts of the 453 instance library in the benchmarks.  ...  Some of the listed programs were tested on a selection of suitable instances and the results published.  ... 
doi:10.1007/s43069-020-0002-0 fatcat:gilnuqtgsvabvh4db2meeo3guq

Penalized Semidefinite Programming for Quadratically-Constrained Quadratic Optimization [article]

Ramtin Madani, Mohsen Kheirandishfard, Javad Lavaei, Alper Atamturk
2020 arXiv   pre-print
Numerical experiments on large-scale system identification problems as well as benchmark instances from the library of quadratic programming (QPLIB) demonstrate the ability of the proposed penalized semidefinite  ...  In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs).  ...  Acknowledgements The authors are grateful to GAMS Development Corporation for providing them with unrestricted access to a full set of solvers throughout the project.  ... 
arXiv:2004.14328v1 fatcat:ibw33jccjndixohorbveqzryya

Polynomial Optimization: Enhancing RLT relaxations with Conic Constraints [article]

Brais González-Rodríguez, Raúl Alvite-Pazó, Samuel Alvite-Pazó, Bissan Ghaddar, Julio González-Díaz
2022 arXiv   pre-print
cone, and semidefinite programming to solve to optimality the instances of well established test sets of polynomial optimization problems.  ...  Additionally, we present a machine learning approach to decide on the most suitable constraints to add for a given instance.  ...  Bissan Ghaddar's research is supported by Natural Sciences and Engineering Research Council of Canada  ... 
arXiv:2208.05608v1 fatcat:uam4mdajbjbghbkrjjqgu2dl2m

Learning for Spatial Branching: An Algorithm Selection Approach [article]

Bissan Ghaddar, Ignacio Gómez-Casares, Julio González-Díaz, Brais González-Rodríguez, Beatriz Pateiro-López, Sofía Rodríguez-Ballesteros
2022 arXiv   pre-print
The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been  ...  To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems.  ...  The third dataset comes from another well known benchmark, QPLIB (Furini et al. 2018) , a library of quadratic programming instances, for which we made a selection analogous to the one made for MINLPLib  ... 
arXiv:2204.10834v1 fatcat:n7g7otcoivamreekhimelkc67q

Parabolic Relaxation for Quadratically-constrained Quadratic Programming – Part II: Theoretical Computational Results [article]

Ramtin Madani, Mersedeh Ashraphijuo, Mohsen Kheirandishfard, Alper Atamturk
2022 arXiv   pre-print
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover  ...  Next, we present numerical experiments on benchmark non-convex QCQP problems as well as large-scale instances of system identification problem demonstrating the efficiency of the proposed approach.  ...  Acknowledgments We are grateful to GAMS Development Corporation for providing us with unrestricted access to a full set of solvers throughout the project.  ... 
arXiv:2208.03625v1 fatcat:ocnojtevrbhyzc27h5nwsjzb2a

A Sublevel Moment-SOS Hierarchy for Polynomial Optimization [article]

Tong Chen, Jean-Bernard Lasserre, Victor Magron, Edouard Pauwels
2021 arXiv   pre-print
We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed as an intermediate (or interpolation) between the d-th and (d+1)-th order SDP relaxations of the Moment-SOS hierarchy  ...  In particular, we provide numerical experiments for d=1 and various types of problems both in combinatorial optimization (Max-Cut, Mixed Integer Programming) and deep learning (robustness certification  ...  Table 5 is a summary of basic information and the number of quadratic, linear, bound constraints of the instances from the QPLIB library.  ... 
arXiv:2101.05167v1 fatcat:3yll3rhssfgd5kwwghi7bqjihu

Faster exact solution of sparse MaxCut and QUBO problems [article]

Daniel Rehfeldt, Thorsten Koch, Yuji Shinano
2022 arXiv   pre-print
Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.  ...  Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse MaxCut and QUBO instances.  ...  Gurobi solves mixedinteger quadratic programs, which are a superclass of QUBO. In fact, the standard benchmark library for quadratic programs, QPLIB (15), contains various QUBO instances.  ... 
arXiv:2202.02305v1 fatcat:uws3ywettjghhin7hbedgjel7q

Digital Annealer for quadratic unconstrained binary optimization: a comparative performance analysis [article]

Oylum Şeker and Neda Tanoumand and Merve Bodur
2020 arXiv   pre-print
For the selective graph coloring problem, we also present a size reduction heuristic that significantly increases the number of eligible instances for DA.  ...  We examine pure QUBO models, as well as QUBO reformulations of three constrained problems, namely quadratic assignment, quadratic cycle partition, and selective graph coloring, with the last two being  ...  The authors would also like to thank Hamed Pouya for useful discussions at early stages of this work.  ... 
arXiv:2012.12264v1 fatcat:ecchf4wojzh3rafb64gwreahpm

New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Loay Alkhalifa, Hans Mittelmann
2022 Mathematics  
Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers.  ...  The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math10020198 fatcat:3eqstp64zjg2rjkgux2uvfgtdi

Compact Disjunctive Approximations to Nonconvex Quadratically Constrained Programs [article]

Hongbo Dong, Yunqi Luo
2018 arXiv   pre-print
nonconvex mixed-integer quadratically constrained programs (MIQCP).  ...  Numerical experiments on synthetic instances used in the literature show that our prototypical implementation (with hundreds of lines of Julia code) can already close a significant portion of gap left  ...  Observing the importance of advancing optimization algorithms for MIQCP, in recent years a specialized instance library named QPLIB [20] (http://qplib.zib.de/) has been developed to hosts a collection  ... 
arXiv:1811.08122v1 fatcat:y22pfg5kzjgnfaa6ohyglocjxu

BiqBin: a parallel branch-and-bound solver for binary quadratic problems with linear constraints [article]

Nicolò Gusmeroli, Timotej Hrga, Borut Lužar, Janez Povh, Melanie Siebenhofer, Angelika Wiegele
2021 arXiv   pre-print
All the main ingredients are carefully developed using new semidefinite programming relaxations obtained by strengthening the existing relaxations with a set of hypermetric inequalities, applying the bundle  ...  Numerical results demonstrate that BiqBin is a highly competitive solver. The serial version outperforms the other three solvers on the majority of the benchmark instances.  ...  Finally, we thank two anonymous referees for improving an earlier version of this work.  ... 
arXiv:2009.06240v2 fatcat:w7rwvcza3jdsbouzxoj3fmepuq

BiqBin: A Parallel Branch-and-bound Solver for Binary Quadratic Problems with Linear Constraints

Nicolò Gusmeroli, Timotej Hrga, Borut Lužar, Janez Povh, Melanie Siebenhofer, Angelika Wiegele
2022 ACM Transactions on Mathematical Software  
All the main ingredients are carefully developed using new semidefinite programming relaxations obtained by strengthening the existing relaxations with a set of hypermetric inequalities, applying the bundle  ...  Numerical results demonstrate that BiqBin is a highly competitive solver. The serial version outperforms the other three solvers on the majority of the benchmark instances.  ...  The main idea underlying this solver is the exact penalty reformulation of a (BQP) instance to an instance of (Max-Cut), introduced by Lasserre and enhanced by two coauthors of this paper in [16] .  ... 
doi:10.1145/3514039 fatcat:hs5nv3fapbhxrce3btqsek6js4

Tightening Discretization-based MILP Models for the Pooling Problem using Upper Bounds on Bilinear Terms [article]

Yifu Chen, Christos T. Maravelias, Xiaomin Zhang
2022 arXiv   pre-print
Compared to a wide range of studies related to methods to convert nonconvex optimization problems into MILPs, research on tightening the resulting MILP models is limited.  ...  These methods convert the original nonconvex optimization problems into mixed-integer linear programs (MILPs).  ...  Instances are modified from the 90 randomly generated instances in D'Ambrosio et al. [DLL11] , which are included in QPLIB, a library of quadratic programming instances [Fur+19] .  ... 
arXiv:2207.03699v1 fatcat:h5uorvpqsnfhnd37vrkh3upise
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