`derivative_options` argument to `minimize` is likely incorrect

[jrmaddison]

e.g. for SciPy's L-BFGS-B using a (non $l^2$) Riesz map will lead to the derivative being supplied to the optimizer being inconsistent. SciPy requires the (non-mapped) derivative.

[Ig-dolci]

Yes, I agree. This was the key reasons I considered adding the derivative option to the minimize. The default Riesz representation in Firedrake is L2, and without the PR 151, we were not able to use SciPy's minimisation with l2 riesz representation because there was no way to set it. I am just thinking why the test is working with scipy using L2.

[jrmaddison]

minimize could access the adjoint variable directly, i.e. use derivative to run the adjoint, but then ignore it's return value and access the Control.block_variable.adj_value directly. That would still cost an extra mass matrix solve but would work without needing to know Firedrake-specific Riesz map parameters.

[jrmaddison]

I am just thinking why the test is working with scipy using L2

The issue is that directional derivatives are evaluated incorrectly. If $\tilde{u}$ and $\tilde{g}$ are dof vectors for a function (direction) and cofunction (derivative) then instead of

$$g(u) = \tilde{g}^* \tilde{u},$$

if we add a Riesz map we (incorrectly) use

$$g(u) = \tilde{g}^* M^{-1} \tilde{u}.$$

This e.g. breaks a line search since it tests derivative values in the wrong direction, but might still happen to work for any specific problem.