Optimization problem using Quasi Newton method

Given x_t and c_mn, the objective function is defined as:

I am trying to solve the above objective function for theta using quasi newton method. But there seem to be some problem with my code as it's not working. Could somebody please help me with this?

Following is my matlab code:

Code for defining objective function:

function f = objfuntc(x_t,c_mn,theta )

L = length(x_t ); 
[M,N] =size(c_mn); 
f = 0 ; 
for t = 1:L 
xs = 0 ;
for n = 1:N 
    for m=1:M
         xs = xs + c_mn(m,n)*exp(1i*2*pi*m*(t - n -2) + theta);
    end
end 
f = f + (x_t(t) - xs)^2 ; 
end

Code for calling objective function:

x_t = rand(16,1 ); 
L = length(x_t);
a = 1;
M = L;
c = rand(M*L/a,1 ); 
c_mn=reshape(c,[M,L/a]);
J = @(theta) objfuntc(x_t,c_mn,theta )
theta0 = 10 ; 
options = optimoptions('fminunc','Algorithm','quasi-newton '); 
[theta, thetaval] = fminunc(J,theta0,options)

[John D'Errico]

Why do you want to write your own optimizer in MATLAB? That is generally a bad idea, when optimization tools written by professionals are readily available.

[christina]

I am using MATLABs fminunc. But my problem is, I can't seem to run the code.

[Torsten]

The variable you want to return from "objfun" is called "J", not "f".

[christina]

Ahh, sorry that was a typo here. I still have the same problem.

[Torsten]

J = @(theta) objfun(x_t,c_mn,theta )

instead of

J = @(theta) objfuntc(x_t,c_mn,theta )

[christina]

Still not fixed.

[Torsten]

Put this code in one file, name it "main.m", open it in MATLAB and run it.

function main
x_t = rand(16,1 ); 
L = length(x_t);
a = 1;
M = L;
c = rand(M*L/a,1 ); 
c_mn=reshape(c,[M,L/a]);
J = @(theta) objfuntc(x_t,c_mn,theta )
theta0 = 10 ; 
options = optimoptions('fminunc','Algorithm','quasi-newton '); 
[theta, thetaval] = fminunc(J,theta0,options)
end

function f = objfuntc(x_t,c_mn,theta )
L = length(x_t ); 
[M,N] =size(c_mn); 
f = 0 ; 
for t = 1:L 
xs = 0 ;
for n = 1:N 
    for m=1:M
         xs = xs + c_mn(m,n)*sin(2*pi*m*(t - n -2) + theta);
    end
end 
f = f + (x_t(t) - xs)^2 ; 
end
end

[christina]

Many thanks, that worked! But if I slightly change the objective function, it shows some error again. I don't understand why. Could you please help me with this?

function main
x_t = rand(16,1 );
L = length(x_t );
a = 1 ;
M = L ;
c = rand(M*L/a,1 );
c_mn=reshape(c,[M,L/a ]);
J = @(theta) objfuntc(x_t,c_mn,theta )
theta0 = 10 ;
options = optimoptions('fminunc','Algorithm','quasi-newton ');
[theta, thetaval] = fminunc(J,theta0,options )
end

function f = objfuntc(x_t,c_mn,theta )
L = length(x_t );
[M,N] =size(c_mn );
f = 0 ;
for t = 1:L
xs = 0 ;
for n = 1:N
for m=1:M
% xs = xs + c_mn(m,n)*sin(2*pi*m*(t - n -2) + theta );
xs = xs + c_mn(m,n)*exp(1i*2*pi*m*(t - n -2) + theta );
end
end
f = f + (x_t(t) - xs)^2 ;
end
end

[Torsten]

x_t and c_mn can be complex-valued ?

You will have to use

f = f + (x_t(t) - xs)*conj(x_t(t) - xs) ;

instead of

f = f + (x_t(t) - xs)^2 ;

Best wishes

Torsten.

[christina]

It can be complex-valued.

[Torsten]

I complemented my comment.

[christina]

Thank you so much! That fixed everything.