Does simulation annealing minimize objective function which has non constant parameter?

Main File

============================

a0 = [.0001 .0001 .0001 .0001 .0001 ];

w = linspace(0,pi,1000);

for i=1:length(w)

w_scal=w(i);

f =@(a)abc(a,w_scal);

[a_vec fval] = simulannealbnd(f,a0);

end

Function File

============================

function ARE = abc(a,w)

ERR = ((1/(j*w)) - ((a(1)*exp(2*j*w) + a(2)*exp(j*w) + a(3)) / (exp(2*j*w)+a(4)*exp(j*w) + a(5)))/(1/(j*w)));

ARE = sum(ERR.^2);

After estimating variables a(1),a(2)..a(5), the ARE's Plot w.r.t w(Omegha)is.

===========================================================================

But The plot should draw like these two graphs.

===============================================

Conclusively, coefficients a(1)....a(5) are not estimated correctly.

Thanks,

Nitin

Answer 1

[Torsten]

I still don't see where you set the variable "j" in your function "abc".

Best wishes

Torsten.

[Nitin Rawal]

The Variable 'j' is a imaginary Unit.

I m using abs() function to calculate absolute value out of a imaginary no.

Thanks, Nitin

[Torsten]

I don't see any abs() function in the definition of ARE...

To minimize a function, it has to be real-valued.

Best wishes

Torsten.

[Torsten]

What you do above does not make sense to me.

For one value of w, you try to estimate 5 parameters a(1),...,a(5) to make ARE minimal.

My guess is that you want to minimize sum_{i=1}^{n} ARE(i)'*ARE(i)

with

ARE(i)= ((1/(j*w(i))) - ((a(1)*exp(2*j*w(i)) + a(2)*exp(j*w(i)) + a(3)) / (exp(2*j*w(i))+a(4)*exp(j*w(i)) + a(5)))/(1/(j*w(i))));

but I'm not sure.

Best wishes

Torsten.