  The focus of this work is on an alternative implementation of the iterative
ensemble smoother (iES). We show that iteration formulae similar to those used
in \cite{chen2013-levenberg,emerick2012ensemble} can be derived by adopting a
regularized Levenberg-Marquardt (RLM) algorithm \cite{jin2010regularized} to
approximately solve a minimum-average-cost (MAC) problem. This not only leads
to an alternative theoretical tool in understanding and analyzing the behaviour
of the aforementioned iES, but also provides insights and guidelines for
further developments of the smoothing algorithms. For illustration, we compare
the performance of an implementation of the RLM-MAC algorithm to that of the
approximate iES used in \cite{chen2013-levenberg} in three numerical examples:
an initial condition estimation problem in a strongly nonlinear system, a
facies estimation problem in a 2D reservoir and the history matching problem in
the Brugge field case. In these three specific cases, the RLM-MAC algorithm
exhibits comparable or even better performance, especially in the strongly
nonlinear system.
