Here is my problem, I’d like to fit some data in order to estimate the parameters of a Logistic function (perhaps 4PL and 5PL).
I am a beginner with mathnet, I think this library has the tools to solve my problem but I do not know how to do.

I left some comments on this problem in this thread:

Also look at the last entry in this thread:

It illustrates the the syntax for a generalized minimum finder. For your purpose, you would have to write a function f that returns the value you want minimized, e.g. the mean squared error of the of your logistic fit using arbitrary input values for a,b,&c. The probably means writing a subroutine that can replace the polynomial in the example. As noted, the good results can depend on good starting values.