Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators (Q452270)

In the paper, a primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators is considered. Various problems already considered in the literature, which the above mentioned problem contains as particular cases, are presented. In the algorithm, the single-valued operators are processed individually via explicit steps, while the set-valued operators are processed implicitly via their resolvents. Thus, this new splitting method can be well used for numerical purposes. This algorithm can also be applied to minimization problems.