Consider the following optimization problem:
$Min\;\;\; CX$
$AX\geq b$
$x_ix_j= x_s x_t\;\;\; i\neq j \neq s\neq t$
$x_j\geq 0;$
Where $A$ is the adjacency matrix and $C$ is a constant vector.
How can one check the feasibility of this optimization problem in an efficient way?