alternative to fmins

[Dominique Richard]

Hello everyboby,

I am using fmins to estimate a set of parameters  by minimizing the error between modelized curves and experimental data.
But I am afraid of not getting the best result and possibly falling into secondary minima.
Is there a way to avoid this pitfall.
More generally are they other functions that I could use instead ot 'fmins' for parameter estimation ?

Schematically my programs consist in 3 scripts:
- main.m for input of data, call of minimization function, output of result
- CSSE.m for computing the errors betwen modelized and experiemental points (the only one fully detailed here)
- model.m for calculating the model points
and they look like this :

main.m

p0 = [p01; p02; p03]; reading experimental data and experimental conditions for each experiment

p = fmins("CSSE", p0, [1;tol;0;0;0;1],[], X, Ydata, Zall, exp, spt)

% where % X is time % Ydata are the experimental points % Zall are the experimental conditions, defined for each experiment % exp are the reference of the experiments % spt is the total number of points saving the results plotting the experimental and modelized (with the optimized set ot parameters) curves plotting the parity curves

CSSE.m

function collected_sum = CSSE_final(p,x,y,Zall,exp,spt)

collected_sum = 0;

nexp = size(exp,1);

for i = 1:nexp

Zrun = Zall((9*(i-1)+1):(9*i),1); % experimental conditions for run #i

Xrun = x(spt(i,1):(spt(i+1,1)-1),1); % time vector for run #i

Yrun = y(spt(i,1):(spt(i+1,1)-1),1); % experimental Cb vector for run #i

%Computation of y with the trial parameters.

[Cb_trial] = model(Xrun,p,Zrun); %

y_trial = Cb_trial';

difference = Yrun - y_trial; % Difference between estimated and experimental data

sum_square_errors = sum(difference.^2); % The sum of the squared errors

collected_sum = collected_sum + sum_square_errors;

endfor

endfunction

model.m

function [Cb] = model(X,p,Z)

calculation of Cb over the time range as a function ot the parameters (p) and the experimental conditions (Z) endfunction

Thank you for your help.