Steepest descent method algorithm

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Luqman Saleem
Luqman Saleem on 17 Sep 2019
Commented: Saleh Msaddi on 9 Mar 2020
For practice purpose, I want to find minima of -humps() function.
I have written the following code but it's not giving correct answer
clear; clc;
%function
f = @(x) -humps(x);
dx = 0.1; %step length
x_current = 1; %starting guess
delta = 1e-4; %threshold value
alpha = 0.1; %finding optimal step length
g = inf; %starting gradient
while norm(g) > delta
%gradient by finite difference
f1 = f(x_current + dx/2);
f2 = f(x_current - dx/2);
g = (f1-f2)/dx;
x_next = x_current-alpha*g; %new solution
x_current = x_next;
fprintf('%d %d\n',x_current,x_next);
x_current = x_next;
end
It give 5.543798e+01 as solution while the solution should either be 0.9 or 0.3 (local and global minimas, respectivily).
Whate am I missing here? can anyone help?

Accepted Answer

Matt J
Matt J on 17 Sep 2019
alpha is too big. Try alpha=0.001.
  2 Comments
Saleh Msaddi
Saleh Msaddi on 9 Mar 2020
In steepest descent, you would always get the local minima. You'd only get the global minima if you start with an initial point that would converge to the global minima; if you're lucky enough. If your stepping size is too small, your solution may converge too slow or might not converge to a local/global minima. On the contradictory, if you choose a big step size, your solution may miss the minimal point.

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