A Branch and Cut Algorithm for NonconvexQuadratically Constrained Quadratic ProgrammingCharles

We present a branch and cut algorithm that yields in nite time, a globally -optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. The idea is to estimate all quadratic terms by successive linearizations within a branching tree using Reformulation-Linearization Techniques (RLT). To do so, four classes of linearizations (cuts), depending on one to three parameters, are detailed. For each class, we show how to select the best member with respect to a precise criterion. The cuts introduced at any node of the tree are valid in the whole tree, and not only within the subtree rooted at that node. In order to enhance the computational speed, the structure created at any node of the tree is exible enough to be used at other nodes. Computational results are reported. Some problems of the literature are solved, for the rst time with a proof of global optimality.