Steepest descent with exact line search method

Noob here . I have been trying to implement steepest descent algorithm on matlab and I first solved it using constant step size. But now I have been trying to implement exact line search method to find the step size which I can't seem to solve . Here's the code I'm working with:

syms x1 x2 
syms alpha  %stepsize

n=input("Enter the roll number:");
f1=(x1-n)^2 + (x2-2*n)^2;
fx=inline(f1);
fobj=@(x)fx(x(:,1),x(:,2));

%Gradient
grad=gradient(f1);
G=inline(grad);
gradx=@(x) G(x(:,1),x(:,2));
%Initial Parameters
x0=[1 1];
k=0;
X=[];


while norm(gradx(x0))>0.001
    
    X=[X;x0];
    gradnew=-gradx(x0);
    a=func(x0,alpha,gradnew,n);
    X_new=x0 + a*gradnew.';
    x0=X_new;
    k=k+1;
end

fprintf("Optimal solution x=%f,%f\n",x0);

fprintf("Optimal value f(x)= %d \n",fobj(x0));
    

function y = func(x,b,d,n)

f=@(a)(x+b.*d' -n).^2 + (x+b.*d'-2.*n).^2;
res=fminunc(inline(f),[1,1])
y=res.b

[Matt J]

I have reformatted your code and put it in a code well:

Answer 1

[Matt J]

n=input("Enter the roll number:");

fobj=@(x) (x(1)-n)^2 + (x(2)-2*n)^2; 
gradobj=@(x)2*[(x(1)-n), (x(2)-2*n)];

x0=[1 1];
k=0;
X=[];


while norm(gradobj(x0))>0.001
    
    X=[X;x0];
    linedir=-gradobj(x0);
    
    fline=@(a) fobj(x0+a*linedir);
    a=fminsearch(fline,0);
    
    x0=x0 + a*linedir;
    k=k+1
end

fprintf("Optimal solution x=%f,%f\n",x0);

fprintf("Optimal value f(x)= %d \n",fobj(x0));

[Rachel Ong]

Can I ask how can this code be applied to a system of more equations? I am new to this and Ive been finding examples but I still do not understand.

[Matt J]

There are no equations in the problem addressed here. This is a cost function minimization problem.

If you have a cost function (and its gradient) that measures agreeement with your equations, it should work just the same.

However, it would be advisable to use fsolve() if you can, rather than implement your own solver.

[Nasser Issa]

Bonjour comment allez-vous je suis nouveau mais je cherche une implémentation sur MATLAB ou en python pour optimisation méthode steepest Descent associé à la méthode dichotomie

J'attends votre réponse sur mon adresse mail [e-mail]