A Simplicial Decomposition-Branch and Price for convex quadratic mixed binary problems

Simplicial Decomposition (SD) is a column generation method which can be useful for convex quadratic problems. In this work we show that this method can be efficiently exploited to solve quadratic convex mixed binary problems, with linear constraints. We propose a Branch-and-Price algorithm, in which at each node we adapt a SD based algorithm. This allows to efficiently reuse the variables generated in one node of the Branch-and-bound tree in its child nodes, providing a speed-up in the overall computing time. We also analyze the interaction of additional techniques for speeding up the overall framework. We provide computational results, which show the efficiency of the proposed method for Quadratic Shortest Path Problems, when compared to the commercial solver Cplex. We also provide some preliminary results for the Quadratic Minimum Spanning Tree Problem.