Solution of the least-squares problem for logistic function

Given the data (pi,ti,fi), i=1,…,m, m>3, we consider the best least-squares approximation of parameters for the logistic function t↦f(t;α,β,γ)=α/(1+eβ−γt), α,γ>0,β∈R. We give necessary and sufficient conditions which guarantee the existence of such optimal parameters.