fsolve terminate far before finding answer when using TolFun option

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hosein bashi
hosein bashi 2021-3-6
评论： hosein bashi 2021-3-8
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
=========================
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

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Matt J
Matt J 2021-3-6
编辑：Matt J 2021-3-7
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.

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