A bottle of OptiClean (UK-made) bought in 1997 goes a long, long way. It cost me $25.00 at the time by mail order and is still in use (about 3ml used—certainly you do not use it slavishly). I have used it on mirrors and eyepieces, brushing it on very lightly (but not edge to edge where it can break and become more difficult to fully remove) and using a small adhesive tab lightly pressed to lift it off when dry. It is said to be a co-polymer and smells suspiciously like nail polish remover (!). The side of the bottle is printed with warnings to avoid naked flames and inhalation (absolutely!). I don't have the original instructions with me but I believe it should not be used on multilayer coated lenses; I certainly do not (it was used last week to remove a stubborn oily stain from a Kenko Zeta UV filter). Might be worth researching.
This link was found during a cursory search to see if OptiClean is still made; apparently yes, and there are warnings that mirror my thoughts.
I have a box of alcohol wipes obtained from the chemist called SkinPrep (photo); these work a treat and completely remove smudges. There are 4 in each of my bags at any time. I use the OptiClean stuff for studio-based maintenance.