ForwardDiff over closed interval

Specific Domains Optimization (Mathematical)
1

I need to optimize a function f(u) defined over a closed domain u =[0,1]. I was happily using Newton’s method and FowardDiff for this until I tried upgrading to v1.0. Now, ForwardDiff intentionally gives the derivative on the right of u. This means that while f(u=1.) is defined, f(u=Dual(1.,1.))=Dual(NaN,NaN).

I see this change marked at the top of the README, but I don’t see any suggestions for how to get the derivative on the left of u or any other “designed” approach to deal with closed domains like this.

2 
function LeftDeriv(f, x)
    ForwardDiff.derivative(t -> -f(-t), -x)
end
3

I just want to mention this as it was much quicker in my use-case: have you tried avoiding autodiff and just using a designated algorithm for a bounded interval, as described in the section “Minimizing a univariate function over a bounded interval” here: Minimizing a function · Optim ? I know this doesn’t address the OP, but might be useful nonetheless

4

This certainly gives the left derivative. However, you will need logic to use right derivatives on the left boundary and left derivatives on the right.

I ended up allowing u to overshoot the interval and then clamp the results later. Clearly, this will not work for functions which are undefined (or without defined derivatives) outside the interval.

5

My use case is pretty specific, so I’m not using Optim.