titel:  The ADMM:  Past, Present, and Future

Jonathan Eckstein, Rutgers University

Over the past 15 years, the alternating direction method of multipliers
(ADMM) has become a standard optimization method.  This talk will cover
the origins of the ADMM, its subsequent development, and what to expect
in the future.

The origins of the ADMM are somewhat unusual in that it was discovered
computationally before it was analyzed.  Its convergence analysis is
also noteworthy because, while the ADMM may outwardly appear to be a
dual ascent method, the natural analyses center on reducing the distance
to certain fixed points combining primal and dual variables.  The nature
of these analyses explains the difficulty of proving convergence of
natural variants of the algorithm that change the penalty parameter
between iterations or involve sums of more than two functions.

We will also cover some currently known variations on the ADMM and the
problem formulation features that tend to distinguish between successful
and unsuccessful applications.  Finally, the talk will briefly address
what we may expect for the future and what other operator splitting
methods might become viable members of the optimization toolbox.