Let $A$ be a positive semidefinite matrix. Also, let $\forall i\in [1,n], x_i \in \{-1,1\}$. And finally, for some of indices $I\subset \{1,\ldots,n\}$, values of $x_i\in \{-1,1\}$ are known. Therefore, the problem is to solve for remaining values of $x_i, i \in \{1, \ldots, n\}-I$. Let $x=[x_1, x_2, \ldots, x_n]$.How to solve the optimization problem $max_x x^\mathsf{T}Ax$ given this constraints?
If one relaxes variables from $x_i \in \{-1,1\}$ to $x_i \in [-1,1]$, how to solve this problem?