appropriate – What does the following error message mean, in the context of NonlinearModelFit?

I deliberately do not include data or a model for this question, since I want a more general answer to be able to solve it myself in the future.

When making an adjustment, usually an adjustment with more than two parameters, I occasionally see the error message:

Search step size has become smaller than tolerance
prescribed by the PrecisionGoal option, but the gradient is larger
than the tolerance specified by the AccuracyGoal option. There is a possibility that the method has stagnated at a point that is not a local minimum.

Most of the time, the adjustment looks good to the naked eye, and the values ​​of the adjusted parameters are reasonable.

So the questions are:

  • What does this error really mean?
  • Does it matter, especially if the adjustment looks good and the adjustment parameters are reasonable? That is, how reliable are the results?
  • How can this error be prevented? I have often played with PrecisionGoal Y AccuracyGoal But it doesn't seem to have much effect.

I appreciate that this problem has solutions that vary according to the individual case, but I often fit very different models and I would like to get some advice on how to avoid such errors and solve them myself, instead of simply posting the problem here.