Extended Linear Formulation for Binary Quadratic Problems

We propose and test a new linearisation technique for the Binary Quadratic Problems (BQPs). We computationally prove that the new formulation, called Extended Linear Formulation, can be effective for different classes of problems in practice. Our tests are based on two sets of classical BQPs from the literature, i.e., the Unconstrained BQP and the Maximum Cut of edge-weighted graphs. Finally we discuss the relations between the Linear Programming relaxations of the different linearisation techniques presented and we discuss the elimination of constraint redundancy which is effective at speeding up the computational convergence.