I have noticed when reading (many) articles about Heston Calibration that not all (few actually) do care about the Feller condition. Below is a compilation of calibration results from some different authors (source):
If we calculate the Feller condition $2 \kappa \theta - \sigma^2$ for the above we can see that in all cases it is extremely close to 0. For row 1, 3 and 6 it is in fact negative.
So the Question is basically: In my own calibration code, should I use the Feller condition as a calibration constraint (e.g. as a penalty function) or should I skip the constraint since it doesn't always hold in the market?
Looking forward to your input!