Does anyone know how to find a feasible solution (or the infeasibility of any solution) in a polynomial time to the following problem:
\begin{align*} xAx^t = 0, \\ Bx^t = c, \\ x_i \ge 0, \end{align*}
where A is not definite positive nor definite negative, but it is symmetric.
Your model allows writing $$y_1^2+y_2^2+\ldots+y_n^2=n,$$ $$-1\leq y_i\leq 1$$ which is equivalent to the statement that each $y_i$ is either $1$ or $-1$, so you can produce an arbitrary number of binary variables in the model.