"plenty" of feasible points is not relevant, because you have provided no evidence that this is true. I see no reason why you draw that conclusion. You have a problem in 20,000 dimensions. That is a huge search space. If you cannot give it a good hint of where to start, AND you have sufficiently problematic constraints, then expect problems.
I would note that if it is so trivial to find a feasible start point, then why did you not provide one?
My guess is that you have equality constraints that may actually preclude any solution, or they are sufficiently constraining that there are far fewer feasible solutions than you apparently expect. Again, 20,000 dimensions is a BIG search space.