Results: The Finite Dimensional Context

What happens if we view the discretized optimization problem as a finite dimensional optimization problem in

and ignore the infinite dimensional nature of the problem?
The figures below show the results for two levels of discretizations. The computed controls exhibit large oscillations, which increase as the discretization is refined. (Note that the two graphs are not on the same scale. Not only do the oscillations increase in frequency, but also in amplitude!) Convergence of the computed controls as the discretization is refined cannot be observed.

Such results are to be expected if off-the-shelf finite dimensional optimization packages are used. This is one of our motivations to incorporate the infinite dimensional problem structure into our TRICE algorithms.