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

作者：Latafat Puya; Patrinos Panagiotis

来源：Computational Optimization and Applications, 2017, 68(1): 57-93.

DOI：10.1007/s10589-017-9909-6

• Convex optimization
• Monotone inclusion
• Operator splitting
• Primal-dual algorithms

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. Our scheme can not be recovered from existing operator splitting methods, while classical methods like Douglas-Rachford and Forward-Backward splitting are special cases of the new algorithm. Asymmetric preconditioning is the main feature of Asymmetric Forward-Backward-Adjoint splitting, that allows us to unify, extend and shed light on the connections between many seemingly unrelated primal-dual algorithms for solving structured convex optimization problems proposed in recent years. One important special case leads to a Douglas-Rachford type scheme that includes a third cocoercive operator.

• 出版日期2017-9