Hi David,
One way to go about the question is to define all the objective functions in a MATLAB function that accepts the parameters, the input data and the output data and return the objective functions as a vector. For example :
function [ rssOutput ] = objFunctions( params,X,Y)
a = params(1); % parameter 1
b = params(2); % parameter 2
rss1 = a.*exp(b.*X) - Y; % objective function 1
rss2 = a.*sin(b.*X) - Y; % objective function 2
rssOutput = [rss1; rss2];
end
Now, initialize the parameters defined in the above function:
x0 = [1,1]'; % initial value of a and b
Then get the input data ('X') and output data ('Y') and then call the ' lsqnonlin ' in the following manner:
x=lsqnonlin(@objFunctions,x0,[],[],[],X,Y);
I have left lower bound , upper bound and options parameters empty for the sake of simplicity right now, but please have a look at the documentation of lsqnonlin , for details more on the same:
This should optimize the parameters over multiple objective functions.
Regards,
Abel Paul Babu
MathWorks.
