Work

A general approach to distributed operator splitting

Year: 2026

Type: article

Abstract: Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone inclusion problems involving both set-valued and single-valued operators, where the latter may lack cocoercivity. Our proposed approach, based on some coefficient matrices, not only encompasses several important existing algorithms but also extends to new ones, offering greater flexibility for different applications. Moreover, by appropriately selecting the coefficient matrices, the resulting algorithms can be implemented in a distributed and decentralized manner.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2026.130692

Authors: Minh N. Dao, Matthew K. Tam, Thang D. Truong

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Australian Research Council

Award: Distributed Optimisation without Central Coordination