  The Augmented Lagrangian Method (ALM) is an iterative method for the solution
of equality-constrained non-linear programming problems. In contrast to the
quadratic penalty method, the ALM can satisfy equality constraints in an exact
way. Further, ALM is claimed to converge in less iterations, indicating that it
is superior in approach to a quadratic penalty method.
  It is referred to as an advantage that the ALM solves equality constraints in
an exact way, meaning that the penalty parameter does not need to go to
infinity in order to yield accurate feasibility for the constraints. However,
we sometimes actually want to minimize an unconstrained problem that has large
quadratic penalty terms. In these situations it is unclear how the ALM could be
utilized in the correct way. This paper presents the answer: We derive a
modified version of the ALM that is also suitable for solving functions with
large quadratic penalty terms.
