I have to maximize the quadratic form $$ {\cal F}={\bf s}^TQ{\bf s} $$ where $Q$ is a finite square matrix such that $Q=Q^\dagger$ and ${\bf s}$ can contain only the values $\pm 1$ as components. The difficulty I met was to fix properly the constraints in such way to maintain the components of the solution ${\bf s}$ to be only $\pm 1$.
Having the correct formulation of the problem through Lagrange multipliers would already be of great help but whatever hint will be appreciated.