Hi, I'm just checking to see if anyone here has an recommendations for software (either a library or possably an actual system) that can handle doing nonlinear optimization that can use derivative information but can handle when they're discontinuous without getting horribly lost. (I'm looking at eventually doing sparse regression where the regularization weight function is $|v|$ or $\sqrt {|v|}$, both of whose derivatives change as $v$ crosses $0$ and have undefined "bidirectional derivatives" at $0$. I'm not actually planning on starting with sparse regression, but as it's something I'd like to try it makes sense to try and start using an optimizer that can eventually handle that.)

If no-one happens to know this I'll look around and record any findings I make here on the forum.