This approach has proven surprisingly effective for many problems. However, as with many heuristic approaches, it is not perfect. It will sometimes fail to converge even for problems known to have solutions
The bottom line, unfortunately, is that we cannot guarantee that the successive approximation approach will successfully handle your specific models. If you encounter problems, you are invited to submit a bug report, but we will not be able to promise a fix.
It is possible, and perhaps “usual”, that the successive approximation method converges to a (the) correct solution (global optimum). It is possible for it to not converge. Is it possible for it to (appear to) converge to a solution which is not a global optimum of the original problem?