Admonish: To warn or notify of a fault; to reprove with mildness, to reprove without harshness. 

Admonish can also mean: To counsel against wrong practices; to caution or advise.  To instruct or direct.

The English word derives from the French admonester, which came from two Latin words.  Ad means: to, toward, or next to.  Monere, means: to advise, to remind, or to warn.

“Admonish your friends privately.  Praise them openly.” 

– Publius Syrus

Don’t bother admonishing your dog, though.