Date: Feb 21, 2013 5:24 AM
Author: pietro
Subject: fmincon: constraint normalization

Hi all, 

I'm using fmincon to optimize an objective function. I need to normalize all the constraints because the design variables have different units (i.e angles, lengths and torque) and I need to check the langrange multiplier otherwise they can't be compared. I normalized the objective function in this way: norm_f(x)=f(x)/f(x0), where f(x) is the objective function, f(x0) is the objective at the initial value and norm_f(x) is the normalzed one. I also normalized the constraint is this way:

Br=repmat(B,1,length(A(1,:)));
An=A./Br;
Bn=ones(length(A(:,1)),1);

where: A and B are the constraint matrices and An and Bn are the normalized one.

the not normalized problem works well, also the one with the normalized objective function and with A and B as constraint matrices. Instead the fully normalized one doesn't work well, despite the normalization seems correct to me, in other words:
isequal(A*x0-B,(An*x0-Bn).*B)

ans =

1

May you be kind to help me in understanding what's wrong with my code?

thank you

Best regards

Pietro