I would say the lens is sharp enough from f/1.7-f/5.6. Maybe the sweet spot is around f/3.5 but then you are chasing that little extra which in this case is such a small extra that it doesn't matter. For real good center sharpness stick between f/2 and f/5.6.
Or, go play with the lens test widget at DPR here.
I tend to use it roughly arround f/3 where it seems sharpest to me but wide opens pretty sharp too - but its such a great lens I find i don't have to worry too much about sharpness - unless u're stopping down massively that is ;-)
Traditionally and as I was taught when studying, the optimum aperture for sharpness on any lens is 2 full stops down from wide open.
The 20mm is an outstanding lens that if used carefully can produce some superb images with a great bokeh, the lens is very sharp wide open so much so that it is often just a case of deciding on depth of field requirements!
I have found that f/2 yields a great results but I don't hesitate to use it wide open either. Otherwise, I just adjust based on the desired DOF rather than "sharpness" or a sweet spot. I shoot my images for the image sake and not the lens' desires
Traditionally the teaching is that tie sweet spot is in the mid point of the f/range. From all the test I have read Panasonic has bumped there sweet spot closer to the wide side of the lens. My 20 mm is very good wide open although there is a softening further off axes, still not very bad. At 2.8 it seems to generally behave very well. My 20 mm is good even at f/16 but not perfect there. On the other hand my 14-45mm is almost too soft at f/16 although still usable.