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Optimization problem using Quasi Newton method

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christina 2018-6-24

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评论： christina 2018-6-25

在 MATLAB Online 中打开

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)

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John D'Errico 2018-6-24

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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 2018-6-24

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

Torsten 2018-6-25

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

christina 2018-6-25

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

Torsten 2018-6-25

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

instead of

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

christina 2018-6-25

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Still not fixed.

Torsten 2018-6-25

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编辑：Torsten 2018-6-25

在 MATLAB Online 中打开

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 2018-6-25

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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