Model solution depends on initial guess?

Hi!

Now that we have a code that computes some criteria for how well the model fits the data I noted that I get slightly different solutions depending on the initial guess I use for the polynomial.

For example when I solve the model using (29,29,0.0001) the criteria is 654.161116361 whereas when I solve it using the same parameters but the initial guess of (27,27,0.215) the criteria is 699.012221248.

The difference is small, but it affects all variables. To see the general fit this probably doesn't matter too much, but I'm worried that this will mess up the minimization routine later. In order to ensure that the model is solved for different parameters we need to change the initial guess when the solver does not find a solution with the initial initial guess we started out with.

Thus my question: is it normal that the solution varies with the initial guess for the polynomial? If yes, is there are way to minimize this error? And if that's not possible, what can we do to stop this from interfering with the estimation?

At the moment the code is written in such a way that the initial guess is always the last initial guess that worked.