writing fmincon funtion in matlab

Hi, Can someone please elp me to do the following optimization problem unsin FMINCON . I have a hard time writng the function that is used in FMINCON.

Thanks

clc;
clear;

p=1;

a0 = 0.1; a1 = 0.4; 

epsi=zeros(3000,1);
simsig=zeros(3000,1);

for i = 1:3000
                 if (i==1) 
                     simsig(i) = a0/(1-a1);
                     s=(simsig(i))^0.5;
                     epsi(i) = normrnd(0,1) * s;
                 elseif (i==2)
                     epsi(i)=epsi(1);
                 else                     
                     simsig(i) = a0+ a1*(epsi(i-1))^2;
                     s=(simsig(i))^0.5;
                     epsi(i) = normrnd(0,1) * s;
                 end
end

yt1=epsi.^2;

ytinitial=yt1(2001:3000);
y=yt1(2001:3000);

len = length(ytinitial);

C = zeros(len,p+1);

C(:,1) = 1; %The first column is for a0
for i = 1:p %Then create shifted columns ( p in number ) for a 
       C(1+i:len,1+i) = y(1:len-i,1);     
end

options =optimset('Display','off','LargeScale','off');

coef = lsqlin(C,ytinitial,[0 1],1,[],[],[0;0],[1;1],[],options);

alpha0 =coef(1);
ar1=coef(2);

Answer 1

[Matt J]

fun=@(x) norm(C*x(:)-ytinitial)^2;

[dav]

thank you much. Can you please explain why you use : in x(:)

[Matt J]

To make sure x ends up being a column vector.

[dav]

Is the method we use here in fmincon different than the method in lsqlin?

ie. is it worth wwhile to use fmincon instead of lsqlin?

Thanks

[Matt J]

I would expect LSQLIN to perform better than FMINCON, at least in terms of speed, because FMINCON has less knowledge of the problem structure, i.e., it doesn't know the problem is linear least squares.

[dav]

thank you very much Matt.

Answer 2

[Alan Weiss]

Check out the definition of the objective function right at the top of the lsqlin function reference page. This should enable you to write the fmincon equivalent, though I do not know why you would want to do so.

Alan Weiss

MATLAB mathematical toolbox documentation

[dav]

I did but, still couldn't figure it out!

I am having trouble writing the "fun" in x = fmincon(fun,x0,A,b)