Steepest descent with exact line search method

Question

Abdul Rahim Shihabuddin 2021-9-15

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1453459-steepest-descent-with-exact-line-search-method

评论： Nasser Issa 2024-2-17

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

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Matt J 2021-9-15

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

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Answer 1

Matt J 2021-9-15

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1453459-steepest-descent-with-exact-line-search-method#answer_787704

编辑：Matt J 2021-9-15

在 MATLAB Online 中打开

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));

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Matt J 2022-2-16

编辑：Matt J 2022-2-16

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 2024-2-17

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 nasserissahamidou@gmail.com

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