This optimization procedure is done to estimate some parameters. The estimates of the parameters are the solutions of a,b,c and d.
I can also estimate the the parameters with an another method (which does not require solution of a system) which I also use these estimates as the initial values for the optimization procedure. Let call this method alternative method.
If I estimate "d" with the alternative method and reduce the number of constraint 3, I get very good results for a,b and c, with optimization procedure using fmincon. The simulations show that estimates of a,b and c are very accurate and also these estimates are also more accurate that the alternative method.
However, if I don't reduce the constraints, and use 4 constraints, the estimates with fmincon are worse than the reduced optimation procedure and also worse than the alternative method.
Why is that? I don't want to reduce constraints. Is there a way to get better estimates without reducing? I will be very glad, if I get any help. Thanks a lot.