[R] Optimization and garch

[stat stat]

Good day,

Here I was trying to write a code for Garch(1,1)     
. As garch problem is more or less an optimization
problem I also tried to get the algorithm for "nlminb"
function. What I saw that if use this function
'nlminb" I can easyly get the estimate of parameters.
But any other function is not working. I tried to
write my own code for optimization using Quasi-Newton
Methods  etc but although it is working for ordinary
non-linear function, it fails in garch case. Therefore
I am trying to get a step by step documentation for
nlminb function. I already gone though its help page
got a look on
"http://netlib.bell-labs.com/cm/cs/cstr/153.pdf>". But
it did not solve my problem. 

In this regards, can anyone give me any step-by-step
approach or theory behind the calculation that
'nlminb" uses? Any help will be highly appreciable.


Thanks and regards,