Optimization

[oyamad]

Now a derivative free bounded univariate optimization function Optim.optimize (Brent()) is used to compute the max in the Bellman operator. This part should be the main bottleneck. It will be more efficient if we utilize information on 1st and 2nd derivatives of f and g.

Options: in ContinuousDP,

1. 1st and 2nd derivatives are mandatory;
2. 1st and 2nd derivatives are optional; in this case, we have to switch the optimization solver depending on whether or not ContinuousDP has derivatives.

[sglyon]

Given that we require users to pass in functions for f and g, we should be able to use automatic differentiation exactly and efficiently calculate the derivatives of f and g.

I think Optim has this functionality built in

[oyamad]

Thanks, I didn't think about automatic differentiation. (And I have no experience with that.)