Yamaha EF2400iS
I used the Honda EU3000 to power my old trailer. At first, it would not start the AC after the AC sat for a while, since the inverter circuitry could not handle the sudden surge requirement to start the compressor 'cold'. I installed an 'easy start kit' in the A/C, and did not have any problems since.
Perhaps the Yamaha doesn't have this problem (thermal cutout in the inverter circuitry too sensitive), or perhaps it is endemic with all inverter generators. There is one generator out there I've heard of which uses the starting battery to give an extra boost to what is being generated; perhaps this would be enought to do the trick.