How to fit parameters of a non-explicit function using the levenberg-marquardt algorithm? Fminsearch does not have it.

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Emanuel Crespo 2017-7-18

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https://ww2.mathworks.cn/matlabcentral/answers/349214-how-to-fit-parameters-of-a-non-explicit-function-using-the-levenberg-marquardt-algorithm-fminsearch

Dear all,

I am trying to fit some model parameters (the model can not be given by an explicit function). For instance, in each iteration I give as an input new parameters that are used by an external program that calculates Values_calc. These values are then compared with Values_exp read from a text file with the deviation between them being the objective function to be minimized. I have been using fminsearch (although already tried patternsearch and global search). The question is (as fminsearch does not have such algorithm) , how can I do such optimization using the levenberg-marquardt algorithm? I know it is existent in lsqnonlin , however it seems to require an explicit function to calculate Values_calc or is just enough to use a function that create the vector Values_calc-Values_exp instead of the AAD?