My idea is now to have two solve functions - one using minerr delivering start values followed by one using find using those start values. |
That will not work. They use the same algorithm (Levenberg Marquardt). The principal difference is that minerr considers the problem solved if the error is minimized, whereas Find only condsiders it solved if the residuals are smaller than CTOL (they actually handle constraints in a different way too). Minerr will head to a local minimum, and then consider that "converged". Find will start in that local minmum, and will then realize it can't reduce the residuals, so it will report a failure to converge.
It is a very difficult problem, and there is no general solution to it (really - if you can figure out a universal way to make non-linear least squares always converge to the global minimum in a reasonable time you will probably get the Nobel prize for Mathematics!).. The best approach depends on the nature of the problem. Without knowing a lot more about the nature of the problem I can only suggest two approaches:
1) Find a linear approximation to the problem, which will have an exact solution. Use that solution as starting guesses.
2) If your iterations are in some sort of sequence, use the solution from one as the starting guesses for the next.
