Newton to see when the Gradient = 0

1 view (last 30 days)
Oskar Soth
Oskar Soth on 5 Jul 2022
Answered: Jan on 5 Jul 2022
Hey i have a Problem i defined the following function:
function Newton(f,df,Hesf,x)
% Newtonverfahren
sigma=1e-4;
beta=0.5;
rho=1e-8;
p=2.1;
eps=1e-6;
kmax=200;
k=0;
fx=feval(f,x);
dfx=feval(df,x);
while norm(dfx) > eps && k<=kmax
Hf=feval(Hesf,x);
if condest(Hf) > 1e+15
d=-dfx;
else
d=(-Hf\dfx')';
if dfx*d' > -rho*norm(d)^p
d=-dfx;
end
end
xd=x+d;
fxd=feval(f,xd);
j=0;
dfxd=dfx*d';
while fxd > fx + sigma * beta^j * dfxd
j=j+1;
xd=x+beta^j*d;
fxd=feval(f,xd);
end
x=xd;
fx=fxd;
dfx=feval(df,x);
k=k+1;
end
disp(x)
%disp(x(1));
%disp(x(2));
end
this is how i defined my functions:
function fx = Rosenbrock(x)
fx=100*(x(2)-x(1)^2)^2+(1-x(1))^2;
end
function dfx=Gradient(x)
dfx=[-400 * x(1) *(x(2)-x(1)^2)+2*(x(1)-1), 200*(x(2)-x(1)^2)];
end
function dfx=Hessematrix(x)
dfx=[-400 *(x(2)-x(1)^2)+800*x(1)^2+2, -400*x(1); -400*x(1), 200];
end
When im now calling the Newton Function with:
Newton('Rosenbrock', 'Gradient', 'Hessematrix', [1.2;1.2])
I get a 2x2 Matrix. But i would expect an output of 2x1 since the output should be the value for the gradient.
I thought maybe something is wrong with my input. Maybe someone can help me

Answers (1)

Jan
Jan on 5 Jul 2022
In the line:
xd=x+d;
x is a [2x1] vector and d a [1x2] vector. The implicite expanding replies a [2 x 2] matrix.
Maybe this fixes the problem:
function dfx=Gradient(x)
dfx=[-400 * x(1) * (x(2)-x(1)^2)+2*(x(1)-1); 200*(x(2)-x(1)^2)];
% ^ instead of a ","
end

Categories

Find more on Get Started with MATLAB in Help Center and File Exchange

Products


Release

R2022a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!