Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications

TL;DR

This paper introduces a flexible primal-dual splitting algorithm for solving complex structured monotone inclusion systems in Hilbert spaces, enabling parallel computation and broad applicability beyond existing methods.

Contribution

It presents a novel primal-dual splitting algorithm tailored for structured monotone inclusions, with comprehensive analysis and diverse applications demonstrating its effectiveness.

Findings

Algorithm converges asymptotically under broad conditions

Supports parallel execution of most steps

Applicable to a wide range of problems in Hilbert spaces

Abstract

A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with linear operators, parallel sums, and Lipschitzian operators. All the operators involved in this structured model are used separately in the proposed algorithm, most steps of which can be executed in parallel. This provides a flexible solution method applicable to a variety of problems beyond the reach of the state-of-the-art. Several applications are discussed to illustrate this point.