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

TL;DR

This paper introduces a primal-dual splitting algorithm capable of efficiently solving complex monotone inclusions involving composite, Lipschitzian, and parallel-sum operators, with applications to convex optimization.

Contribution

It presents a novel parallel primal-dual splitting algorithm that handles mixed monotone operators and extends existing methods for structured inclusion problems.

Findings

Algorithm processes Lipschitzian operators explicitly.

Most steps of the algorithm are parallelizable.

Effective for convex minimization problems.

Abstract

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents. In addition, the algorithm is highly parallel in that most of its steps can be executed simultaneously. This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods. The application to convex minimization problems is given special attention.