optimization with Levenberg-Marquardt algorithm

Hi everyone! I have a function f(x) (ex: f(x)=3+sin(2x)-exp(-x)) and it's experimental value Fexp (ex:0.02344). So how I can find x that minimize the difference f(x)-Fexp using Levenberg-Marquardt algorithm in Toolbox optimization? Many thanks

[Matt J]

Levenberg-Marquardt would be overkill. Since it's a 1D problem, you could just use fzero().

[ghazal mohamed]

hi Matt,thank you for your comment, the function given is just an example, the expression I want to minimize is more complicated than that. On the other hand I am not looking for zero of function, simply because f(x)-Fexp (in my case) dosen't have zero so I am looking for x that gives the smallest value of f(x)-Fexp using Levenberg-Marquardt algorithm.

Answer 1

[Alan Weiss]

I am not sure that I understand you, but perhaps you are asking about Curve Fitting Via Optimization.

You are free to use the Levenberg-Marquardt algorithm in lsqcurvefit or lsqnonlin when fitting a nonlinear function to data. See the Algorithm option.

Alan Weiss

MATLAB mathematical toolbox documentation

[ghazal mohamed]

Hi Alan,thank you for your reply, I am not looking for data fitting. I have function f(x) and an experimental value Fexp, if I consider g(x)=f(x)-Fexp, x is a variable in [0 100], g(x) takes differet values depending on x, among these values (of g) there is a minimum :gmin, gmin is obtained when x=Xm so I am looking for this value Xm. (I think that I can't use a nonlinear solver because g(x) has not zero but there is a minimum value..).