We present a numerical method for the
minimization of constrained optimization problems
where the objective is augmented with large quadratic
penalties of inconsistent equality constraints. Such ob-
jectives arise from quadratic integral penalty methods
for the direct transcription of optimal control prob-
lems. The Augmented Lagrangian Method (ALM) has
a number of advantages over the Quadratic Penalty
Method (QPM). However, if the equality constraints
are inconsistent, then ALM might not converge to a
point that minimizes the bias of the objective and
penalty term. Therefore, we present a modification of
ALM that fits our purpose. We prove convergence of
the modified method and bound its local convergence
rate by that of the unmodified method. Numerical
experiments demonstrate that the modified ALM can
minimize certain quadratic penalty-augmented func-
tions faster than QPM, whereas the unmodified ALM
converges to a minimizer of a significantly different
problem.