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 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