  In a recent work (arXiv-DOI: 1804.08072v1) we introduced the Modified
Augmented Lagrangian Method (MALM) for the efficient minimization of objective
functions with large quadratic penalty terms. From MALM there results an
optimality equation system that is related to that of the original objective
function. But, it is numerically better behaved, as the large penalty factor is
replaced by a milder factor.
  In our original work, we formulated MALM with an inner iteration that applies
a Quasi-Newton iteration to compute the root of a multi-variate function. In
this note we show that this formulation of the scheme with a Newton iteration
can be replaced conveniently by formulating a well-scaled unconstrained
minimization problem.
  In this note, we briefly review the Augmented Lagrangian Method (ALM) for
minimizing equality-constrained problems. Then we motivate and derive the new
proposed formulation of MALM for minimizing unconstrained problems with large
quadratic penalties. Eventually, we discuss relations between MALM and ALM.
