Script too Long to Run

I've just finish creating the script on one of the Optimisation Method. The problem that I currently have is the script took around 20 minutes

I've also preallocate changing vectors, but that hasn't made any difference. Not sure what I can do to resolve this?

clear
clc
format long 

syms X1 X2 X3 X4 real;

%Preallocating changing vectors
x1=zeros(10000,1);
x2=zeros(10000,1);
x3=zeros(10000,1);
x4=zeros(10000,1);
error=zeros(10000,1);

A=[1 0 -1 3; 0 2 1 0; -1 1 6 -1; 3 0 -1 10];
b=[0; -2; -1; -1];
X=[X1; X2; X3; X4];

f=@(X1, X2, X3, X4) (1/2)*X'*A*X + b'*X;
x1(1)=0; x2(1)=1; x3(1)=0; x4(1)=0;

g=A*X+b;
alpha=0.1;
tol=10^(-6)
k=1;
gl = subs(g, [X1, X2, X3, X4], [x1(k), x2(k), x3(k), x4(k)]);

while norm(gl)>tol
    
    gl = subs(g, [X1, X2, X3, X4], [x1(k), x2(k), x3(k), x4(k)]);
    alpha=gl'*gl./(gl'*A*gl);
    x1(k+1)=x1(k)-alpha*gl(1);
    x2(k+1)=x2(k)-alpha*gl(2);
    x3(k+1)=x3(k)-alpha*gl(3);
    x4(k+1)=x4(k)-alpha*gl(4);
    error(k)=norm(gl);

    k=k+1;
end

[Stephen23]

"Not sure what I can do to resolve this?"

Don't use the symbolic toolbox. Numeric operations are much faster.

[Charles Thomas]

Thank you very much! Just removed "syms", and made some few changes before running the loop. Never realise that is the cause of the immeasurable run time for my script, but I really appreciate your help.

Answer 1

[Sulaymon Eshkabilov]

Here is a little simplified version of your code:

clc
format long 
n=1e4;
x1=zeros(n,1);
x2=x1;
x3=x1;
x4=x1;
error=x1;
A=[1 0 -1 3; 0 2 1 0; -1 1 6 -1; 3 0 -1 10];
b=[0; -2; -1; -1];
x1(1)=0; x2(1)=1; x3(1)=0; x4(1)=0;
g=@(y1,y2, y3, y4)(A*([y1; y2; y3; y4])+b);
alpha=0.1;
tol=1e-6;
k=1;
gl =g(x1(k), x2(k), x3(k), x4(k));
while norm(gl)>tol
    gl = g(x1(k), x2(k), x3(k), x4(k));
    alpha=gl'*gl./(gl'*A*gl);
    x1(k+1)=x1(k)-alpha*gl(1);
    x2(k+1)=x2(k)-alpha*gl(2);
    x3(k+1)=x3(k)-alpha*gl(3);
    x4(k+1)=x4(k)-alpha*gl(4);
    error(k)=norm(gl);
    k=k+1;
end