admm decomposition

This paper addresses distributed minimization of the sum of local objective functions over multi-agent networks subject to global coupling constraints. We propose a primal-dual algorithm based on a newly defined Lagrangian function and, for the first time, rigorously establish its linear convergence via time-scale separation theory—without requiring strong convexity or smoothness assumptions on individual objectives. The algorithm natively supports asynchronous communication and exhibits inherent robustness to packet loss, eliminating the need for synchronization protocols or retransmission mechanisms. Methodologically, it unifies the ADMM-based consensus framework with nonlinear systems analysis tools. We validate its efficacy in a three-phase low-voltage microgrid auxiliary service scenario. Compared to existing distributed optimization methods, our approach achieves provable linear convergence while significantly enhancing stability and practicality under non-ideal communication conditions.

This work addresses primal-dual optimization in distributed empirical risk minimization, aiming to unify the theoretical understanding of CoCoA and ADMM-type algorithms. Methodologically, we reformulate the dual problem and establish a unified primal-dual update framework. Our key contribution is the first rigorous proof that CoCoA is equivalent to proximal ADMM under a specific choice of the augmented Lagrangian penalty parameter. Furthermore, we demonstrate that judicious tuning of this parameter substantially improves both convergence rate and communication efficiency for various ADMM variants—including consensus, linearized, and proximal ADMM—rendering them uniformly superior to standard CoCoA. We provide a unified convergence analysis with non-asymptotic guarantees. Extensive experiments on synthetic and real-world datasets empirically validate the superiority of parameter-tuned ADMM variants. This work offers new theoretical insights and practical guidance for algorithm selection and design in distributed learning.

To address excessive communication overhead in asynchronous ADMM for distributed optimization and federated learning, this paper proposes Quantized Asynchronous ADMM (Q-Async-ADMM), which integrates coarse low-bit quantization into the variable exchange phase. The method preserves both asynchrony and convergence guarantees while drastically reducing inter-node data transmission. We establish theoretical convergence under nonconvex and nonsmooth objectives. Empirical evaluation across multiple federated learning and distributed training tasks demonstrates 75–90% reduction in communication volume, with convergence speed and accuracy matching full-precision baselines; the approach further exhibits strong scalability to complex models such as deep neural networks. To our knowledge, this is the first work to systematically incorporate coarse quantization into the asynchronous ADMM framework, yielding an efficient and robust distributed optimization paradigm tailored for communication-constrained environments.

This work investigates the stability of primal-dual gradient flow dynamics for multi-block composite convex optimization under generalized consensus constraints, particularly targeting large-scale distributed settings involving multiple nonsmooth terms. We propose a continuous-time dynamical framework based on the proximal augmented Lagrangian and establish global exponential convergence via Lyapunov analysis. Compared with mainstream discrete-time algorithms such as ADMM and EXTRA, our approach significantly relaxes standard assumptions—namely, strong convexity and smoothness of objective components, as well as algebraic connectivity of the communication graph—and further proves the necessity of certain relaxed conditions. The theoretical results provide milder, more broadly applicable convergence guarantees for distributed nonsmooth optimization. Numerical experiments demonstrate the efficiency and practicality of the proposed dynamics in both parallel and distributed implementations.

In multi-source heterogeneous systems (e.g., supply chains), primal, dual, and proximal agents coexist with immutable interfaces—yet existing consensus optimization methods, such as standard ADMM, assume agent homogeneity and cannot accommodate such heterogeneity. Method: We propose the first distributed consensus planning framework supporting collaborative optimization among all three agent types. By unifying linearized ADMM, dual ascent, and standard ADMM, we design a novel relaxation-and-enhancement update mechanism that accommodates structural mismatches without requiring interface modifications. Contribution/Results: Under mild assumptions, we establish rigorous convergence: O(1/k) rate under weak convexity and two-step linear convergence under strong convexity. Experiments on mixed-agent scenarios demonstrate both robustness and efficiency, validating the framework’s plug-and-play applicability. This work provides the first theoretically grounded, algorithmically practical solution for decentralized decision-making in heterogeneous multi-agent systems.

This work proposes an online learning strategy for accelerating the convergence of the Alternating Direction Method of Multipliers (ADMM) when solving structured convex optimization problems—such as time-varying quadratic programs arising in model predictive control—by dynamically tuning its relaxation parameter. The approach targets scenarios where the problem structure remains fixed but parameters change over time, thereby circumventing the need for costly matrix refactorizations typically required in conventional penalty parameter adjustment. For the first time, convergence guarantees are established for ADMM with time-varying penalty and relaxation parameters. By integrating ideas from reinforcement learning into parameter scheduling, the method achieves substantial improvements in solution efficiency while maintaining low computational overhead. Implemented within the OSQP framework, the proposed strategy significantly reduces both iteration counts and actual solve times on standard quadratic programming benchmarks.

This study addresses the slow convergence and high communication overhead of ADMM in distributed optimal transport over bipartite graphs by proposing the DAP-ADMM algorithm. The method introduces a solver-free projection routine and an adaptive penalty mechanism based on local KKT residuals, combined with accelerated preconditioning techniques, to achieve fully decentralized computation for unbalanced mass allocation using only neighbor-to-neighbor communication. Theoretically, global convergence is established along with an O(1/k) convergence rate bound. Empirical evaluations demonstrate that the proposed algorithm significantly outperforms standard distributed ADMM, yielding substantial improvements in both computational and communication efficiency.

为解决异构边缘网络中ADMM同步实现效率低的问题，提出P-GADMM方法，通过基于计算能力的分组和云层有界异步协调来优化。

This study addresses the challenges of heterogeneous client computing capabilities and communication bottlenecks that hinder distributed optimization in edge networks by proposing the WQ-GADMM algorithm. This method introduces a novel Group Alternating Direction Method of Multipliers framework integrating windowed scheduling and bidirectional quantization. By synergizing computation-time-based client grouping, window activation, and quantized transmission for collaborative updates, it significantly reduces communication overhead while tolerating bounded model staleness and inexact local updates. The convergence bound with respect to the KKT residual is theoretically derived. Experimental results demonstrate that 12-bit quantization substantially decreases communication volume and latency, achieving full group coverage while preserving model accuracy.

This work addresses the challenge of continuous trajectory optimization in non-convex environments by proposing a joint discrete–continuous optimization framework based on the Alternating Direction Method of Multipliers (ADMM). The approach parameterizes trajectories as polynomials and introduces a spatiotemporal allocation graph to model coupled spatiotemporal constraints. By integrating mixed-integer programming with shortest-path search, the method enables efficient solution computation. In contrast to conventional decoupled strategies, the proposed framework substantially expands the feasible search space and achieves stable convergence from arbitrary initial conditions without requiring complex warm-start procedures. Experimental results demonstrate significant improvements in both solution quality and robustness.