I have a similar problem. Using the garch-function from the package t-series,
there is sometimes the warning "false convergence" in the output. In other
cases, this warning is not given and instead there is the message "relative
function convergence". The problem is that this happens with the same
parameters of the time series(simulated with the same parameters). Sometimes
this message disappears, if the function receives different start values
from the user. 

My question is: Should I still use this function or is this a real problem?
Is this message about false convergence something to worry about?

I would be very thankful for an answer.

Regards,
L.Gottehrer
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