[JustFinishedBSG]

> on-smooth functions like abs(), max(), min() where derivatives do not exist

While these functions are not differentiable they are sub-differentiable. Which is an extension of differentiability.

Subderivatives are set, if the set only contain one point the function is differentiable. Otherwise it doesn't matter for gradient descent you can just use any element of the set.

> Disjoint IF-THEN-ELSE conditions are discontinuities in the function space

Same, it doesn't matter, they mathematically are equivalent to indicator functions and are subdifferentiable.

https://en.wikipedia.org/wiki/Subderivative