why there is a different value between the latest Fval and the Optimal Solution that Fmincon gives me

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crime Adrian on 22 Nov 2021
Commented: crime Adrian on 23 Nov 2021
The output that Fmincon gives to me are correct absolutely，but when I check the iterations， at the latest iteration ,Fval=3.742029e-12,which is not the optimal function value:x=(1,1),fun=0,the Fval should be 0 instead of 3.742029e-12. How Fincon gets the optimal solution x=(1,1)
here are my codes:
lb=[-5,-5];
ub=[5,5];
fun = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
A = [];
b = [];
Aeq = [];
beq = [];
x0 = [0.0,0.0];
nonlcon = [];
options = optimoptions('fmincon','Display','iter','Algorithm','sqp');
x= fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options) Alan Weiss on 22 Nov 2021
The answer is correct to within tolerances. Generally, you cannot expect an answer that is correct down to the last few decimal places. To learn more ablut what you can expect from floating-point calculations, see
Alan Weiss
MATLAB mathematical toolbox documentation
crime Adrian on 23 Nov 2021
Thanks a lot !!!