Spectral bounds for unconstrained (-1,1)-quadratic optimization problems

Given an unconstrained quadratic optimization problem in the following form:with , we present different methods for computing bounds on its optimal objective value. Some of the lower bounds introduced are shown to generally improve over the one given by a classical semidefinite relaxation. We report on theoretical results on these new bounds and provide preliminary computational experiments on small instances of the maximum cut problem illustrating their performance.