fsolve terminate far before finding answer when using TolFun option

fsolve terminate far before finding answer when using TolFun option. I wrote a simple code to show my problem:

======================================

clc
clear
Opt=optimoptions('fsolve','Tolfun',1);
x0=10;
x_solution=fsolve(@fff,x0,Opt);

function y=fff(x)
y=x^2;
end

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x_solution=6.5

6.5^2=42.5 and is far from (Tolfun=1)

Can anyone help me to know how should I solve this issue. Thanks a lot

Answer 1

[Matt J]

Can anyone help me to know how should I solve this issue

You should make TolFun a lot smaller.

Note that x_solution and TolFun are not related in magnitude, so there is no expectation that 6.5^2 should be close to TolFun. TolFun relates to the value of the objective function. Also, note from this table,

https://www.mathworks.com/help/optim/ug/tolerance-details.html

that TolFun is not an absolute tolerance in fsolve, so with TolFun=1 it only means that the change in the cost function as a fraction of the current cost function value has fallen below 1.

[hosein bashi]

yes you are right.Thanks alot