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## On the Solution of Nonconvex Cardinality Boolean Quadratic Programming problems

### Citations

113 | Scip: Solving constraint integer programs. Mathematical Programming Computation 1 - Achterberg - 2009 |

69 |
A survey for the quadratic assignment problem
- Loiola, Abreu, et al.
- 2007
(Show Context)
Citation Context ...cterization of the polytope of an unconstrained BQP. Important real world applications of BQP include a class of problems on facilities location, the so called Quadratic Assignment Programming (QAP) (=-=Loiola et al., 2007-=-), tasks allocation (Billionnet et al., 1992), and molecular conformation (Phillips and Rosen, 1994). In this work the focus is on the computational solution of a specific class of Cardinality BQP (CB... |

58 | Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing - Pardalos, GP - 1990 |

54 | The Boolean quadric polytope: some characteristics, facets and relatives - Padberg - 1989 |

47 | Relation Between MILP Modelling and Logical Inference for Chemical Process Synthesis
- Raman, Grossmann
- 1991
(Show Context)
Citation Context ...ariable zij and the following inequalities are added: zij ≥ xi + xj − 1, ∀i < j (1) zij ≤ xi, ∀i < j (2) zij ≤ xj, ∀i < j. (3) The inequalities above can also be derived from the logical proposition (=-=Raman and Grossmann, 1991-=-): xi ∧ xj ⇔ zij, 1 ≤ i < j ≤ n, (4) or derived using the Reformulation-Linearization Technique (RLT) of Sherali and Adams (1998) from the following equations: zij ≥ max { xlixj + xix l j − xlixlj, xu... |

39 | Converting the 0-1 polynomial programming problem to a 0-1 linear program - Glover, Woolsey - 1974 |

25 | A quadratic assignment formulation of the molecular conformation problem
- Phillips, Rosen
- 1994
(Show Context)
Citation Context ...include a class of problems on facilities location, the so called Quadratic Assignment Programming (QAP) (Loiola et al., 2007), tasks allocation (Billionnet et al., 1992), and molecular conformation (=-=Phillips and Rosen, 1994-=-). In this work the focus is on the computational solution of a specific class of Cardinality BQP (CBQP) problems defined as: min{cTx+ xTQx : x ∈ Bn,M}, (P1) where Bn,M = { x : ∑ 1≤x≤n xi =M } ∩Bn : B... |

19 | On nonconvex quadratic programming with box constraints - Burer, Letchford |

19 | Experiments in quadratic 0-1 programming - Barahona, Jünger, et al. - 1989 |

16 |
An efficient algorithm for task allocation problem
- Billionnet, Costa, et al.
- 1992
(Show Context)
Citation Context ...trained BQP. Important real world applications of BQP include a class of problems on facilities location, the so called Quadratic Assignment Programming (QAP) (Loiola et al., 2007), tasks allocation (=-=Billionnet et al., 1992-=-), and molecular conformation (Phillips and Rosen, 1994). In this work the focus is on the computational solution of a specific class of Cardinality BQP (CBQP) problems defined as: min{cTx+ xTQx : x ∈... |

16 | Compact linearization for binary quadratic problems - Liberti |

13 | An evolutionary algorithm for polishing mixed integer programming solutions - Rothberg |

12 | Cut-polytopes, Boolean quadric polytopes and nonnegative quadratic pseudo-Boolean functions - BOROS, HAMMER - 1993 |

10 | A simultaneous lifting strategy for identifying new classes of facets for the boolean quadric polytope - Sherali, Lee, et al. - 1995 |

9 | Different formulations for solving the heaviest k-subgraph problem - BILLIONNET |

9 |
Floudas. GloMIQO: Global mixed-integer quadratic optimizer
- Misener, A
(Show Context)
Citation Context ...convex CBQP; examples include CPLEX, GUROBI, XPRESS and SCIP (Achterberg, 2009). In addition, nowadays there are several solvers available such as BARON (Tawarmalani and Sahinidis, 2005), or GloMiQO (=-=Misener and Floudas, 2012-=-), which can rigorously address nonlinear combinatorial problems. Therefore, based on the many options available to solve CBQP involving common available software, our goal is to identify the best app... |

7 |
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
- Bruglieri, Ehrgott, et al.
- 2006
(Show Context)
Citation Context ...tions are described and the problem is characterized. Typical applications include problems in edge-weighted graphs (see Billionnet (2005) for a detailed description), and facility location problems (=-=Bruglieri et al., 2006-=-). The objective of this work is to evaluate the practical options available to solve CBQP problems using the common available software. In the last decades significant theory has been developed to ch... |

7 |
Cardinality constrained Boolean quadratic polytope, Discrete Applied Mathematics 79
- Mehrotra
- 1997
(Show Context)
Citation Context ...he convex hull of the BQP and CBQP have been studied using polyhedral theory and convex analysis. An important remark is that important results valid for the BQP polytope are also valid for the CBQP (=-=Mehrotra, 1997-=-). Padberg (1989) is a classic reference on the characterization of the convex hull of the BQP problem, and has proposed three families of facets: triangle, clique, cut, and generalized cut inequaliti... |

5 | 2009, Improved compact linearizations for the unconstrained quadratic 0–1 minimization problem - Hansen, Meyer |

2 | A linearization framework for unconstrained quadratic (0-1) problems - Gueye, Michelon - 2009 |

2 | Chemical Engineering Greetings to Prof. Sauro Pierucci, chap. Computational advances in solving Mixed Integer Linear Programming problems. AIDIC - Lima, Grossmann - 2011 |

1 | Experiments in quadratic 0-1 programming - F, Reinelt - 1989 |

1 |
A polyhedral approach for a constrained quadratic 0-1 problem
- Faye, Trinh
- 2005
(Show Context)
Citation Context ... the fact that (F1) considers the two additional constraints: zij ≤ xi and zij ≤ xj . The formulation (F2) has one more constraint, the star inequality, that is known to be a strong valid inequality (=-=Faye and Trinh, 2005-=-), which leads to an improved relaxation. Therefore, the following relation is valid: W0 ≤ W1 ≤ W2. The formulation (F3) is equal to the formulation (F2) minus the constraint zij ≥ xi+xj−1. It will be... |

1 | An evolutionary algorithm for polishing mixed integer programming solutions - unknown authors |