Semidefinite relaxations for mixed 0-1 second-order cone program
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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 (MQP) be a general mixed integer quadratic program that consists of minimizing a quadratic function subject to linear constraints. In this paper, we present a convex reformulation of (MQP), i.e. we reformulate (MQP) into an equivalent program, with a convex objective function. Such a reformulation can be solved by a standard solver that uses a branch and bound algorithm. We prove that our reformulation is the best one within a convex reformulation scheme, from the continuous relaxation point of view. This reformulation, that we call MIQCR (Mixed Integer Quadratic Convex Reformulation), is based on the solution of an SDP relaxation of (MQP). Computational experiences are carried out with instances of (MQP) including one equality constraint or one inequality constraint. The results show that most of the considered instances with up to 40 variables can be solved in 1 h of CPU time by a standard solver.