Asymmetric forward-backward-adjoint splitting for solving monotone inclusions involving three operators

In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint Splitting (AFBA), for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical operator splitting methods, like DouglasRachford (DRS) and Forward-Backward splitting (FBS) are special cases of our new algorithm. Among other things, AFBA unifies, extends and sheds light on the connections between many seemingly unrelated primal-dual algorithms for solving structured convex optimization problems, proposed in the recent years. More importantly AFBA greatly extends the scope and the applicability of splitting techniques to a wider variety of problems. One important special case leads to a generalization of the classical ADMM for problems with three (instead of two) blocks of variables.