Now I’m dealing with a feasibility-check problem, but it has a non-convex constraint. Is there a method can deal with this problem?
This was already addressed in your previous question For feasibility-check problem, if I use SCA(successive convex approximation) for one of the non-convex constraint, do I have to finish the whole SCA process? .
In general, if you want reliable determination of feasibility for a non-convex problem, use a global optimizer or constraint solver. CVX is not the right tool for this job.