Is there an efficient algorithm for this quadratic constraint problem?

Question

I have a problem that can be formulated as a quadratic constraint program with $O(n^3)$ constraints and $O(n)$ variables, which are grouped into $O(n)$ vectors of size 2. The constraints are all of the form $s((x_j-x_i)\cdot(x_k-x_i))\geq0$ where $s\in\{-1,1\}$ and the $x_i,x_j,x_k$ are distinct vectors of variables. Is there a way to take advantage of this special structure to get a more efficient solution to the problem than general quadratic constraint programs?