Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
The basic algorithm for pseudo-Boolean programming revisited
Selected papers on First international colloquium on pseudo-boolean optimization and related topics
Lagrangian decomposition for integer nonlinear programming with linear constraints
Mathematical Programming: Series A and B
A new lower bound for the quadratic assignment problem
Operations Research - Supplement
An efficient algorithm for a task allocation problem
Journal of the ACM (JACM)
A decomposition method for quadratic zero-one programming
Management Science
A branch-and-cut algorithm for the equicut problem
Mathematical Programming: Series A and B
Semidefinite programming in combinatorial optimization
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Best reduction of the quadratic semi-assignment problem
Discrete Applied Mathematics
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Solving Graph Bisection Problems with Semidefinite Programming
INFORMS Journal on Computing
Discrete location problems with push-pull objectives
Discrete Applied Mathematics
Upper bounds and exact algorithms for p-dispersion problems
Computers and Operations Research
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
Mathematical Programming: Series A and B
Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs
Discrete Optimization
A computational study on the quadratic knapsack problem with multiple constraints
Computers and Operations Research
An efficient compact quadratic convex reformulation for general integer quadratic programs
Computational Optimization and Applications
On valid inequalities for quadratic programming with continuous variables and binary indicators
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Test-assignment: a quadratic coloring problem
Journal of Heuristics
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Let (QP) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear equality constraints. In this paper, we present QCR, a general method to reformulate (QP) into an equivalent 0-1 program with a convex quadratic objective function. The reformulated problem can then be efficiently solved by a classical branch-and-bound algorithm, based on continuous relaxation. This idea is already present in the literature and used in standard solvers such as CPLEX. Our objective in this work was to find a convex reformulation whose continuous relaxation bound is, moreover, as tight as possible. From this point of view, we show that QCR is optimal in a certain sense. State-of-the-art reformulation methods mainly operate a perturbation of the diagonal terms and are valid for any {0,1} vector. The innovation of QCR comes from the fact that the reformulation also uses the equality constraints and is valid on the feasible solution domain only. Hence, the superiority of QCR holds by construction. However, reformulation by QCR requires the solution of a semidefinite program which can be costly from the running time point of view. We carry out a computational experience on three different combinatorial optimization problems showing that the costly computational time of reformulation by QCR can however result in a drastically more efficient branch-and-bound phase. Moreover, our new approach is competitive with very specific methods applied to particular optimization problems.