Links between linear bilevel and mixed 0-1 programming problems
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Grasp and Path Relinking for 2-Layer Straight Line Crossing Minimization
INFORMS Journal on Computing
A polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
Perspective cuts for a class of convex 0–1 mixed integer programs
Mathematical Programming: Series A and B
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
An algorithm for the generalized quadratic assignment problem
Computational Optimization and Applications
GRASP with path-relinking for the generalized quadratic assignment problem
Journal of Heuristics
Extending the QCR method to general mixed-integer programs
Mathematical Programming: Series A and B
A probabilistic heuristic for a computationally difficult set covering problem
Operations Research Letters
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We address the exact solution of general integer quadratic programs with linear constraints. These programs constitute a particular case of mixed-integer quadratic programs for which we introduce in Billionnet et al. (Math. Program., 2010) a general solution method based on quadratic convex reformulation, that we called MIQCR. This reformulation consists in designing an equivalent quadratic program with a convex objective function. The problem reformulated by MIQCR has a relatively important size that penalizes its solution time. In this paper, we propose a convex reformulation less general than MIQCR because it is limited to the general integer case, but that has a significantly smaller size. We call this approach Compact Quadratic Convex Reformulation (CQCR). We evaluate CQCR from the computational point of view. We perform our experiments on instances of general integer quadratic programs with one equality constraint. We show that CQCR is much faster than MIQCR and than the general non-linear solver BARON (Sahinidis and Tawarmalani, User's manual, 2010) to solve these instances. Then, we consider the particular class of binary quadratic programs. We compare MIQCR and CQCR on instances of the Constrained Task Assignment Problem. These experiments show that CQCR can solve instances that MIQCR and other existing methods fail to solve.