Do fminsearch tolerances give the range?

Dear Friends,

I am trying to understand the physical meaning of tolerances used in the function fminsearch. I am using an example from the web address http://www.mathworks.com/help/matlab/math/example-curve-fitting-via-optimization.html.

If the default tolerances are 1e-4 and the optimization provides best fit values for "A" and "lambda," can I say A is plus or minus 1e-4 and lambda is plus or minus 1e-4? How can I state the possible range of A and lambda?

Thank you for your help.

Kind regards, Aaron

Answer 1

[Alan Weiss]

The meaning of TolX and TolFun for most optimization solvers is depicted here toward the bottom of the page. fminsearch stops when the simplex is small and when the difference between the largest and smallest objective function values in the simplex is small, too. For details, edit fminsearch, and look near line 300 of the code.

Now just because these differences are small, it does not mean that the true minimum is close to the returned value fval. It also does not follow that the point where the true minimum is obtained is anywhere near the returned point x.

The tolerances are stopping criteria, and they apply to the values that the fminsearch simplex algorithm generates. It is very hard to know in general how these values relate to the optima for an arbitrary function. If the objective function is smooth and convex near the value fminsearch returns, then you might be able to say something along the lines you are looking for, that the true optimum is near the point x. But in general, you don't know.

Alan Weiss

MATLAB mathematical toolbox documentation