Optim function in R is not converging to the parameters that minimize the error at every iteration, which could be a sign of different parameters producing the same curve, and R isn't able to agree on what are the best possible parameters.
What alternatives/different methods could be tried to avoid this?
The alternative is the identification of non-significant parameters. When you have non-significant parameters in a non-linear least squares problems, the non-significant parameters can take any value and produce the same value of objective function. Therefore you must identify the non-significant parameter in your model and eliminate them. The mathematical procedure for to identify non-significant parameter in a non-linear least square problem require the evaluation of Jacobean matrix with the variation of each response with respect to each parameter and perform a statistic test. The details of procedure can be consulted in,
https://doi.org/10.1016/j.jfoodeng.2018.09.004
When we are facing a parameter in a certain model, one of the possible ways to handle such problems is to perform what we call stability set analysis on them.The stability set of the first kind for such parametric models can be obtained in the following way:Solve the problem for a given value of the parameter, obtain an optimal solution(or any other output), then determine the set of all parameters that keep the same optimal solution.After that select another value of the parameter outside the obtained set and repeat this process several times till the whole parametric space is exhausted.
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