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

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)

Answer 1

[Alan Weiss]

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

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal?s_tid=srchtitle

https://www.mathworks.com/matlabcentral/answers/437670-i-checked-calculation-and-found-the-solution-does-not-accord-with-the-equation?s_tid=srchtitle

Alan Weiss

MATLAB mathematical toolbox documentation

[crime Adrian]

Thanks a lot !!!