optimization with Levenberg-Marquardt algorithm

2018 1 23
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更新时间：2018 1 24
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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

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Matt J
Matt J 2018-1-23
Levenberg-Marquardt would be overkill. Since it's a 1D problem, you could just use fzero().
ghazal mohamed
ghazal mohamed 2018-1-24
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.

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Alan Weiss
Alan Weiss 2018-1-24
编辑：Alan Weiss 2018-1-24

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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

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ghazal mohamed
ghazal mohamed 2018-1-24
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..).

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