fminbnd fails to converge with exitflag=1

Question

John 2012-7-6

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https://ww2.mathworks.cn/matlabcentral/answers/42970-fminbnd-fails-to-converge-with-exitflag-1

I'm trying to use fminbnd to find the extrema of a function, but I'm having an issue with the tolerance. Here is a simple example:

>> [x,fval,exitflag]=fminbnd(@cos,3,4,optimset('TolX',1e-12))
x = 3.1416
fval = -1
exitflag = 1
>> x-pi
ans = 4.3792e-10

The exitflag indicates that fminbnd converged within the specified tolerance. So why is x-pi>TolX???

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Answer 1

Anton Semechko 2012-7-7

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because TolX is a measure of change in x between two successive iterations and not an indication of how close it is to a true minimum, which is generally not known

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Anton Semechko 2012-7-9

Sorry, can't help you here. You got to take this issue up with the MathWorks folks.

Alan Weiss 2012-7-9

在 MATLAB Online 中打开

Thanks for the excellent question. You found an error in the documentation. I will address this error soon.

In fact, if you look at the code for fminbnd by executing "edit fminbnd", you see that there is a tolerance of TolX and also a value sqrt(eps) that comes into play. The true final tolerance relates to

sqrt(eps)*x + TolX/3

where x is the current point. Now sqrt(eps) ~ 1e-8, so if you choose a TolX any smaller than that, and x ~ 1, then the value of TolX has almost no effect.

Alan Weiss

MATLAB mathematical toolbox documentation

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