A distributed augmented Lagrangian decomposition algorithm for constrained optimization

TL;DR

This paper introduces a new distributed optimization algorithm based on the augmented Lagrangian method, with accelerated variants and hierarchical coordination, validated through theoretical analysis and numerical experiments.

Contribution

It presents a novel distributed augmented Lagrangian decomposition algorithm with convergence guarantees and accelerated variants, unifying existing theories within the AL framework.

Findings

Proposed DALD algorithm with rigorous convergence proof

Accelerated variants improve efficiency in early iterations

Validated effectiveness through numerical experiments

Abstract

Within the framework of the augmented Lagrangian (AL), we propose a novel distributed optimization method, termed Distributed Augmented Lagrangian Decomposition (DALD), and provide a rigorous convergence proof for its standard version. To address the high iteration costs in early stages, we propose several accelerated variants of DALD that enhances efficiency without compromising theoretical guarantees, supported by a comprehensive convergence analysis. To facilitate the description of the distributed optimization process, the concept of hierarchical coordination networks is introduced, integrating hierarchical matrix concepts to aid in this explanation. We further explore and expand the applicability of the DALD method and demonstrate how it unifies existing distributed optimization theories within the AL framework. The effectiveness and applicability of the proposed distributed optimization method and its variants are further validated through numerical experiments.