How to perform multivariable calibration

Hello,

I'd like to perform a multivariable calibration. I used to compute single variable calibration using "lsqnonlin" or "fminsearch" but it's my first multivariable calibration...

My calibration is quite simple. I have a price equal to a sum of other instrument prices. Theses prices are computed using a function. One of this function's parameters is the parameter that I'd like to calibrate. For example :

X = F_1(a_1,b_1,c_1,...) + F_2(a_2,b_2,c_2,...) + F_3(a_3,b_3,c_3,...) + .....

I'd like to find a_1, a_2, a_3, ... in the previous function. All the other parameters and X are known.

Does anyone knows a function that allows to perform such a calibration?

In a previous version, I used "lsqnonlin" but I had to compute my calibration assuming that a_1 = a_2 = a_3 = ... = A which is not true in my case.

Many thanks in advance, Paul