  In this work we propose a new splitting technique, namely Asymmetric
Forward-Backward-Adjoint splitting, for solving monotone inclusions involving
three terms, a maximally monotone, a cocoercive and a bounded linear operator.
Classical operator splitting methods, like Douglas-Rachford and
Forward-Backward splitting are special cases of our new algorithm. Asymmetric
Forward-Backward-Adjoint splitting unifies, extends and sheds light on the
connections between many seemingly unrelated primal-dual algorithms for solving
structured convex optimization problems proposed in recent years. More
importantly, it greatly extends the scope and applicability of splitting
techniques to a wider variety of problems. One important special case leads to
a Douglas-Rachford type scheme that includes a third cocoercive operator.

Optimization and Control