Distributed and Decentralized Optimization Algorithms via Consensus ALADIN
For researchers and practitioners in distributed optimization, this work provides a more communication-efficient and computationally lighter alternative to existing decentralized algorithms, though it is an incremental extension of the ALADIN framework.
This paper extends the ALADIN framework to propose Consensus ALADIN (C-ALADIN) for distributed consensus optimization, with both first-order and second-order variants, and a decentralized version over directed graphs with quantized communication. Numerical results show fast convergence with reduced communication and computational costs compared to existing methods.
Distributed optimization has found widespread applications in smart grids, optimal control, and machine learning. This paper studies distributed consensus optimization. We extend the Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) framework to propose Consensus ALADIN (C-ALADIN) with a central coordinator, which directly handles consensus constraints. Our C-ALADIN algorithm admits both a first-order variant and a second-order variant that employs a Hessian approximation, avoiding direct transmission of second-order information while preserving fast local convergence. We then develop a decentralized version of C-ALADIN that operates over directed graphs with quantized communication, using a finite-time coordination protocol. For both versions, we establish global convergence guarantees for convex problems and local convergence guarantees for non-convex problems. For the decentralized case, the iterates converge to a neighborhood of the optimum determined by the quantization level. Numerical results demonstrate that our methods retain fast convergence while substantially reducing communication and computational costs compared to existing decentralized approaches.