  This thesis presents new mathematical algorithms for the numerical solution
of a mathematical problem class called \emph{dynamic optimization problems}.
These are mathematical optimization problems, i.e., problems in which numbers
are sought that minimize an expression subject to obeying equality and
inequality constraints. Dynamic optimization problems are distinct from
non-dynamic problems in that the sought numbers may vary over one independent
variable. This independent variable can be thought of as, e.g., time.
  This thesis presents three methods, with emphasis on algorithms, convergence
analysis, and computational demonstrations. The first method is a direct
transcription method that is based on an integral quadratic penalty term. The
purpose of this method is to avoid numerical artifacts such as ringing or
erroneous/spurious solutions that may arise in direct collocation methods. The
second method is a modified augmented Lagrangian method that leverages ideas
from augmented Lagrangian methods for the solution of optimization problems
with large quadratic penalty terms, such as they arise from the prior direct
transcription method. Lastly, we present a direct transcription method with
integral quadratic penalties and integral logarithmic barriers. All methods are
motivated with applications and examples, analyzed with complete proofs for
their convergence, and practically verified with numerical experiments.
