This is a bit nitpicky, but so you're aware: the term is differentiable, not derivable. You differentiate a function, you don't derive it.

Essa é uma questão lingüística, não matemática.

Em português há uma diferença diminuta de sentido entre "diferenciável" e "derivável" (na Análise Matemática mesmo), mas não recordo mais qual.

O inglês sendo o idioma mutante que é, talvez acabe absorvendo essa diferença de nomenclaturas dessa forma: derivable x differentiable.

I understand that it is simply a difference of language and that the intent is the same, but in mathematics precision of language is incredibly important. This is a common error in English.

I just want to reflect on the irony of your having no trouble replying to a comment in Portuguese about how it's important to use the right term. This whole thing has brightened my day.

Translation:

That's a linguistic question, not a mathematics one.

In Portuguese there's a very small difference between "differentiable" and "derivable" (in the context of Math Analysis), but I don't recall it.

English being a mutable language, may end up absorbing the difference between nomenclatures in that way (??): derivable x differentiable.

Sorry French guy here. Wrong translation . Thanks for pointing out

Are you serious? https://en.wikipedia.org/wiki/Mathematical_optimization

Just using gradient based descent can not achieve much with non-convex functions.

I don't think that the GP meant "optimize by gradient descent." I think the intention was in saying that a problem that is differentiable (or sub-differentiable, if locally convex, say) gives a lot more structure to the program than a general non-differentiable one.

Yes, while optimizing both might still be NP-hard (e.g. an ILP vs. an arbitrary polynomial, say, both of which are non-convex), we usually don't have nearly as much problem optimizing differentiable programs of the same size as some combinatorial optimization problems simply because the structure allowed by the differentiable one is so much nicer and we can find local minima without a problem (which is usually enough for most practical cases).