Steepest descents methods algoritme for higher dimensional objective functions

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Clarisha
Clarisha 2024-10-21
评论： Matt J 2024-10-23
Hello,
I am trying to apply the steepest descent method on a function with 10 variables.
With 2 variables it is easy as I can split the problem. Now I tried to write this algoritme for a vector, but without succes.
In the following code you will first see a simple steepest descent algorithm and in the code below you see a similar algoritme based on a vector as input, especially needed to tackle higher dimensional problems, by using the vector notation in this algoritm.
Can I have some feedback.
Clarisha
clc
close
clear
%objective function
b=@(x,y) (1-x).^2+(y-x.^2).^2
%de gradient
dbdx=@(x,y) (2-4*x)-4*x*(y-x.^2)
dbdy=@(x,y) 2*(y-x.^2)
%initials
x0=20
y0=20
%proces
for i=1:10
s1=dbdx(x0,y0);
s2=dbdy(x0,y0);
xd=@(d) x0+d*s1;
yd=@(d) y0+d*s2;
bd=@(d) b(xd(d),yd(d));
d_star=fminsearch(bd,0)
x1=xd(d_star);
y1=yd(d_star) ;
iteratie=i
x0=x1%update initials
y0=y1%update initials
ObjectiveValue=b(x0,y0)
end
%********************************************************************************************************
%Steepest descent method for functions with more input.
B=@(X) (1-X).^2;
DBDX=@(X) -2*(1-X);
X0=[0 0]; %initials
for iteration=1:N
S=DBDX(X0);
XK=@(D) X0+D.*S;
BK=@(D) B(XK(D));
D_STAR=fminsearch(BK,X0);
X=XK(D_STAR)
X0=X
end
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Clarisha
Clarisha 2024-10-21
Thank you for your quick response. I am actually trying to solve a PDE constraint problem with numerical methods. So I splitted the problem in two and one of the parts is optimizing an unconstrainted multidimensional function. As I am not so experienced in programming, I tried the steepest descent problem first. But what other methods would you suggest?
Clarisha
Clarisha 2024-10-21
For your information I also tried the conjugate gradient method and a gmres code. And chose for the one I could best interprete in matlab.

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Matt J
Matt J 2024-10-21
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Clarisha
Clarisha 2024-10-22
Thank you for the references. I just skipped the steepest descent method and used the fiminunc().
Matt J
Matt J 2024-10-23
You're welcome, but please Accept-click the answer to indicate that it resolved your question.

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更多回答（1 个）

Walter Roberson
Walter Roberson 2024-10-21
fminsearch() uses simplex algorithm, not Steepest Descent.
One implementation of Steepest Descent is https://www.mathworks.com/matlabcentral/answers/787539-steepest-descent-algorithm-in-matlab#answer_1191330
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Matt J
Matt J 2024-10-21
But I think here fminsearch is being used to do the 1D line search step of steepest descent.
If so, it probably would have been better to use fminbnd.
Clarisha
Clarisha 2024-10-21
Yes I read somewhere that the fminbind () is used for 1 dimensional problems. But infact I have a multivariate fcostunction with more than 30 dimensions (variables) and I am looking for the combination of these 30 variables that optimizes my costfunction.

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