Optimization

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.

Start in ContinuousDP and trace the Bellman operator's use of Optim.optimize and Brent(). Review how f and g are represented and whether derivative information is currently exposed. Define and implement the derivative-aware solver choice, with the existing derivative-free path preserved when derivatives are unavailable; verify the optimization behavior and performance.