If there is someone replying to your posts with insults (public or private), just report the person, ignore him or her and go on about your own business.
Such people are likely feeding in some sick, twisted way off the attention you give, and will likely stop once they realize that they can no longer goad anyone into responding.
Even if you try to reason with the troll, or politely request the troll to stop, he or she will likely get a thrill from even that much attention, as small as it is.
So heed my request, and please ...
Thank you.