Leasts-squares gradient-free optimization

Hello all,

I've been trying to fit parameters of my model to experimental data (9 parameters), I can set up a least squares problem and solve it with the SNOPT algorithm. The only thing is that some parameters aren't changed, whereas I can go in by hand and change them and there is a significant difference. Is there some way to do an optimization that doesn't rely on gradients with least squares, or am I missing something with the solver?

Thanks,
Aaron R. Shifman