Steepest descent method algorithm

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Luqman Saleem
Luqman Saleem 2019-9-17
评论： Saleh Msaddi 2020-3-9
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?

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采纳的回答

Matt J
Matt J 2019-9-17
alpha is too big. Try alpha=0.001.
  2 个评论
Luqman Saleem
Luqman Saleem 2019-9-17
编辑：Luqman Saleem 2019-9-17
@Matt J It worked. I am so stupid.
With initial guess = 0, the solution converges to 0.3 (global minima) while with guess=1, the solution is 0.9 (local minima).
Do you know any way to bypass local minima and get to global minima always? I am trying to understand multiscaling, can you help me understanding this.
Thank you very much.
Saleh Msaddi
Saleh Msaddi 2020-3-9
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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