Im trying to use gradient decent with a for loop to determine the value of x that minimizes the function

Im trying to use gradient descent to numerically determine the value of x that

minimizes the function f(x) = x^2 − 3x + 1 with its derivative f(x) = 2x − 3.

Starting from x(0) = 0, im trying to plot the value of the

function f(x) as a function of the number of iterations for a few different

values of α.

This is my current code:

clc, clearvars, close all

iterations = 10;

alpha = 0.15;

x = zeros(iterations,1);

x(1) = -1;

for k = 2:iterations

x(k) = x(k-1) - alpha*( 2*x(k)-3 )

end

figure(1)

plot(k,x)

figure(2)

plot(x1,f_x)

Im not sure how to plot this, after its calculated i could use f= x.^2-3*x+1 to calculate its function value.

Any ideas how i could make it work?

Answer 1

[David Hill]

iterations = 10;
alpha = 0.15;                         
x = zeros(iterations,1);              
x(1) = -1;                     
      
for k = 2:iterations                  
    x(k) = (x(k-1)+alpha*3)/(1+2*alpha);  
end
plot(x)

Answer 2

[Torsten]

f = @(x) x.^2 - 3*x + 1;
iterations = 15;
alpha = 0.15;                         
x = zeros(iterations,1); 
x(1) = 0;
for k = 2:iterations                  
   x(k) = x(k-1) - alpha*(  2*x(k-1)-3  )  ;
end
 
figure(1)
hold on
plot(x,f(x),'o')
xplot = linspace(0,2,100);
yplot = f(xplot);
plot(xplot,f(xplot))
hold off
grid on

figure(2)
plot(1:iterations,x,'o')
grid on