Unconstrained formulation of standard quadratic optimization problems

A standard quadratic optimization problem (StQP) consists of nding the largest or smallest value of a (possibly indenite) quadratic form over the standard simplex which is the intersection of a hyperplane with the positive orthant. This NP-hard problem has several immediate real-world applications like the Maximum-Clique Problem, and it also occurs in a natural way as a subproblem in quadratic programming with linear constraints. We propose unconstrained reformulations of StQPs, by using dierent approaches. We test our method on clique problems from the DIMACS challenge.