Find minimum Sum while keeping variable fix

Hi guys,

I need a little help with my optimization problem.

I need to find the values of Parameters a and b, such that sum of squared residuals is minimized but while the average of the transformed vector is equal to a given value.

I try to run it with fmincon but this doesn't seem to work for the equality constraint.

function [SSE]=logit3(Par,x)
if nargin<5;
    ir=0;  %default ir=0
end;

if rows(Par)<cols(Par); % put parameters in column
    Par=Par';
end;
if rows(Par)~=3; % check for the the right number of parameters as inputs
error('Dimension of Par not compatible');
end;
%% Assign the Parameters to the Elements in the Vector
a=Par(1);
b=Par(end-1);
meanpd=Par(end);
%%
T=rows(x);
y=zeros(T,1);
res=zeros(T,1);
for i=1:T
  y(i)= (1/(1+exp(-(a+b*x(i)))));
  res(i)=(y(i)-1).^2;
end
meanpd=mean(y);
SSE=sum(res);

end

Answer 1

[Alan Weiss]

I don't see your equality constraint. If the equality constraint is a nonlinear constraint, you need to pass it in the fmincon nonlcon argument. If it is a linear constraint, pass it as Aeq-beq arguments.

If you need more info or I have misunderstood you, please show us your fmincon call as well as your objective function call.

Alan Weiss

MATLAB mathematical toolbox documentation

[Andrea D'Amato]

Indeed I didn't put the constraint since I use this code as a fucntion to transform my variable x in a logit.

In my "main" code I used this code:

% x is variable
Par=[1;1;0.05];
Aeq=[0 0 1];
beq=0.05;

options=optimset('Display','iter','Algorithm','interior-point','TolFun',0.000001,'TolX',0.000000001,'MaxFunEvals',1000);
[theta]=fmincon('logit3',Par,[],[],Aeq,beq,[],[],[],options,x);