The development of numerical methods for finding optimal solutions
of control problems modeled by differential-algebraic equations (DAEs)
is an important task. Usually restrictions are placed on the DAE such
as being semi-explicit. Here the numerical solution of optimal control
problems with linear time-varying DAEs as the process and quadratic cost
functionals is considered. The leading coefficient is allowed to be
time-varying and the DAE may be higher index. Both a direct transcription
approach and solution of the necessary conditions are examined for two
important discretizations.