Quasi newton method for optimization

I am trying to solve the above objective function for theta using quasi newton method. But I am getting the following error. Can somebody please help me fix this error?

Following is my matlab code:

Code for defining objective function:

 function f = objfun(x_t,c_n,theta)
  t=0:length(x_t)-1;
  L=length(t);
  n=0:length(c_n)-1;
  N=length(n);
  for i=1:L
      for j=1:N

          f=@(theta) sum((x_t(i)-sum(c_n(j).*exp(-((t(i)-n(j)*a)^2/theta^2))))^2)

end
end

   end

Code for calling objective function:

    a = 1;
    x_t=rand(32,1);
    c_n=rand(32,1);

f = @(theta) objfun(x_t,c_n,theta)

theta0 = 20;
options = optimoptions('fminunc','Algorithm','quasi-newton');
[theta, thetaval] = fminunc(f,theta0,options)

%

Answer 1

[Alan Weiss]

Try this for your function:

function f = objfuntc(x_t,c_n,theta)

L = length(x_t);
N = length(c_n);
f = 0;
for t = 1:L
    xs = 0;
    for n = 1:N
        xs = xs + c_n(n)*exp(-(((t-n)/theta)^2));
    end
    f = f + (x_t(t) - xs)^2;
end

Call it like this:

a = 1;
x_t = rand(32,1);
c_n = rand(32,1);
f = @(theta) objfuntc(x_t,c_n,theta)
theta0 = 20;
options = optimoptions('fminunc','Algorithm','quasi-newton');
[theta, thetaval] = fminunc(f,theta0,options)

Alan Weiss

MATLAB mathematical toolbox documentation

[HN]

Alan Weiss ,

What if one wants to see all the values of theta and function evaluated values ?

I've some similar problem. I would love to post my question if you have time to share your thoughts.

Thank you

[Alan Weiss]

Are you talking about a history of the iterations? Use an output function. This example has an output function with some history; adapt it as you like.

Alan Weiss

MATLAB mathematical toolbox documentation

[HN]

My function has three optimization parameters . These are rp, alpha and beta. The objecive function f is evaluated for minimal output. These three variables must simultaneously create a grid and the the function will be evaluated with every point and check for minimum. Is this quasi-newton algorithm ok for this problem Alan Weiss ? How about my program ? is it right ?

Thank you

function f= objfun(rp,alpha,beta)

        rp=1000;      % initial value 
        L=1000;       % leg length - Equal for all legs
        alpha=2*pi/3; % intial vlaue 
        beta=4*pi/3;  % intial vlaue 
        z=707.1068;   % Height the platform
        ts=1/50;
        t=0:ts:1;
for k=1:length(t)
    for j=1:length(t)
        th(j)=-0.2*cos(2*pi*t(j));
        psi(k)=0.2*sin(2*pi*t(k)); 
        phi(j)=atan2(sin(psi(k))*sin(th(j)),(cos(psi(k))+cos(th(j))));
        R=Rot('y',th(j))*Rot('x',psi(k))*Rot('z',phi(j));
        x(k)=1/2*rp*(-cos(phi(j))*cos(psi(k))+cos(phi(j))*cos(th(j))+sin(phi(j))*sin(psi(k))*sin(th(j)));
        y(k)=-rp*cos(psi(k))*sin(phi(j));
        
        Gcc=[Gc(1:3,1:2),Gc(1:3,6)]
        C(:,:,:)=pinv(-Gcc)*Gcp        % matrix  
        f=@(rp,alpha,beta) sum((C'*C)*vp)   % objective function 
        
        
    end 
end 
end 

[Alan Weiss]

Sorry, I don't know what you are asking. Please start a new question with a clear problem statement.

Alan Weiss

MATLAB mathematical toolbox documentation

[HN]

Ok, thank you.

Answer 2

[victor d]

In my Research (data in Excel format )

5 independent variables

1 dependent variables.

So i need to do the following neural Network algorithms.

1.Backpropagation algorithms

2.conjugate gradient method

3.Quasi-Newton method