Interface to optimization and AD

[mjyshin]

Since differential programming is all the rage in Julia, do you think it will one day be possible to use nonlinear optimization packages where objective functions include ApproxFun Funs? Here is a simple case study where this feature can be useful. This may be more of an issue to raise on, say, Optim and Zygote's pages, but I was wondering if you had thought of the feasibility of it given the infinite-dimensional nature of the operators. Thank you in advance!