[Help] Optimization with Matlab

[Buulong Nguyen <buulong@dutmpw1.tudelft.nl>]

Dear friends,

I would like to know how to optimize three vectors at the same time using 
Matlab.

PROBLEM DESCRIPTION:

We have designed a tool for measuring dielectric properties of oil-saturated
porous media. The equipment measures the scatter function of an EM wave
transmitted alongs a coaxial line. 

The measured scatter function differs however from the actual one because 
of (mainly) three types of frequency-dependent errors: the directivity error 
Ed(f); the frequency response error Ef(f) and the source match error Es(f).
>From the theory of network analysis, the actual scatter function S_act and 
the measured one S_meas are related to each other by:

       S_meas(f) = Ed(f) + {[S_act(f) * Ed(f)]/[1 - Es(f) * S_act(f)]}

or:

       S_act(f) = [Smeas(f) - Ed(f)]/{Es(f)*[S_meas(f) - Ed(f)] + Ef(f)}

In the ideal case (no errors) Ed(f)=Es(f)=0 and Ef(f)=1. 

In order to find out Ed(f), Es(f), and Ef(f) we measure the scatter 
functions (S_meas) in three standard media (with well-known dielectric 
properties). On the other hand, we calculate the theoretical scatter
function (S_th) of those standard media. 

Now we have for every frequency three equations with three unknown 
variable: Ed(f), Es(f), Ef(f). We want to solve those equation 
by optimizing Ed, Es and Ef in such a way that the difference between 
S_act calculated with the formulae above and S_th is minimum. 


QUESTIONS:

- I understand the FMINS function in Matlab can be only used to optimize 
a function F(X)=0 with a starting vector Xo. FMINS attempts to return a 
vector X which is a local minimizer of F(X) near Xo.
How can I optimize at the same time the three vectors Ed(f), Es(f) and Ef(f)?
Should I use another optimization tool? So yes, which one?

- I'm also failled in using FSOLVE to optimized a matrix consisting of 
the three vectors. 

- Is there another way to determine Ed(f), Es(f) and Ef(f) based on the 
measused and calculated data?

I really appreciate your prompt reply and any advice.

Thank you very much for taking these views into consideration.

Regards, Buu-Long