Direct transcription with collocation-
type methods (CTM) is a popular approach for solving
dynamic optimization problems. It is known that these
types of methods can fail to converge for problems that
feature singular-arc solutions, high-index differential-
algebraic equations and over-determined constraints.
Recently, we proposed the use of quadrature penalty
methods (QPM) as an alternative numerical approach
to collocation-type methods. In contrast to the concept
of collocation, which requires constraint-residuals to
equal zero at individual points (e.g. at collocation
points), the main idea of QPM is to simply oversample
this number of points and use their respective quadrature weights in a quadratic penalty term, coining
the name of quadrature penalty. In this paper, we
provide numerical case studies and a broad numerical
comparison on a wide range of problems, highlighting
the benefits of QPM over CTM not only in difficult
problems, but also in solving problems competitively to
CTM. These results show that QPM can be considered
an attractive first go-to method when solving general
dynamic optimization problems.