Estimation method for ETAs with POSTHOC

Dear NMusers, I have two questions about the mathematical details on POSTHOC estimation in NONMEM. How does NONMEM actually do when doing POSTHOC ($EST METHOD=0 MAXEVEL=0) to get ETAs? I assume but not for sure there is an objective function to be minimized, somewhat like: Objective function = SUM(Yobs-Ypred)^2/sigma^2 + SUM(Para_i-Para_pop)^2/omega^2 Is there an objective function used in NONMEM when doing POSTHOC? If so, what is that function? Secondly, if the answer to above is yes, let’s assume the real objective function is the same as what I mentioned above. I wonder how (NONMEM does) to minimize this function? I am currently trying to do similar things in R/Python language. I tried Metropolis-Hasting algorithm and Simulated Annealing algorithm, but with some technical problems. And the result was not comparable with NONMEM as well. Can someone give me a direction for this? The more mathematically detailed the better. Thanks! Warm regards, Tingjie