I am currently solving an indefinite quadratic program with linear constraints using CPLEX. Moreover, I am trying to determine whether the candidate point CPLEX is feeding my callback function is an extreme point.
I know that a certain $x \in \mathbb{R}^n$ is an extreme point if and only if there is equality in at least $n$ linearly independent rows in the inequality $A x \le b$, but I do not know how to guarantee that the constraints I feed CPLEX (also the ones it generates itself) are linearly independent with respect to the other constraints in the model.
My question thus is: How do I check in CPLEX (or another off-the-shelf MIQP solver) whether a certain candidate $x$ is an extreme point?