Inverter Surge Capacity -Technique Behind it
There are protection circuits associated with most practical inverters. The simplest protection circuit would just limit the maximum current to the maximum steady-state current. That sort of circuit would protect the inverter but would trip if the inverter was not grossly overrated for loads that have a surge at start, such as motors, compressors and the like. 

However, the inverter circuit will not immediately fail due to short term loading somewhat in excess of what it can sustain indefinitely. It takes time for the parts to heat up to the point where damage occurs. 

So a more sophisticated protection circuit that trips immediately on heavy overload or short and allows a moderate overload to persist for some time will allow the inverter to be used for such a load. You could use a state observer to model the thermal response if you have a microcontroller, estimating the real-time junction temperature (for example) based on measurable variables, and tripping at the appropriate time.