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dealing with the convergence status

Hervé CHAPUIS 
Hi everyone,

I am using lmer (and glmer) in a simulation study in order to find the 
best experimental design.
Using gaussian deviates I simulate a population and  I analyse the data 
with a mixed model.
I repeat these operations many times (about 5000 replicates)  in order  
to derive trends and distributions of parameters.

My problem is that  I sometimes run into false convergences. I have a 
warning message but that's all.
"Il y a eu 50 avis ou plus (utilisez warnings() pour voir les 50 premiers)"

Is there a way to obtain the convergence status of the lmer/glmer models 
in a tractable way so that I  do not account for this replicate in case 
of false  convergence ? Given the large number of replicates, I do not 
run the program interactively.

I hope I made it clear.
Many thanks.