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?
Feasibility checking
optimization;nonlinear programming;convex optimization