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Online distributed optimization algorithm with dynamic regret analysis under unbalanced graphs

AUTOMATICA 2025年 174卷

作者： Yao, Songquan Xie, Siyu Li, Tao East China Normal Univ Sch Math Sci Shanghai 200241 Peoples R China Univ Elect Sci & Technol China Sch Aeronaut & Astronaut Chengdu 611731 Peoples R China

We consider online distributed convex optimization problems with a sum of locally dynamic loss functions under unbalanced graphs. When optimizing the dynamic local loss function, every node tracks the time-varying global optimal solution by communicating with neighboring nodes via communication networks in a cooperative way. We propose a novel online distributed Push-Pull algorithm and present that the proposed online optimization algorithm can track the dynamic optimal solution with proper step sizes. We analyze the dynamic regret of the proposed algorithm in two cases where the global loss function is strongly convex and smooth, or is convex, smooth and Lipschitz. Our results illustrate that the dynamic regret of the proposed online optimization algorithm can be sublinear, if the path length and the gradient variance are sublinear. At last, we demonstrate the property of the online distributed optimization algorithm by two simulation examples. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Dynamic regret distributed optimization Convex optimization Online learning Online push-pull algorithm

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Exponential Convergence of Primal-Dual Dynamics Under General Conditions and Its Application to distributed optimization

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第4期35卷 5551-5565页

作者： Guo, Luyao Shi, Xinli Cao, Jinde Wang, Zihao Southeast Univ Sch Math Nanjing 210096 Peoples R China Southeast Univ Sch Cyber Sci & Engn Nanjing 210096 Peoples R China Yonsei Univ Yonsei Frontier Lab Seoul 03722 South Korea

In this article, we establish the local and global exponential convergence of a primal-dual dynamics (PDD) for solving equality-constrained optimization problems without strong convexity and full row rank assumption on the equality constraint matrix. Under the metric subregularity of Karush-Kuhn-Tucker (KKT) mapping, we prove the local exponential convergence of the dynamics. Moreover, we establish the global exponential convergence of the dynamics in an invariant subspace under a technically designed condition which is weaker than strong convexity. As an application, the obtained theoretical results are used to show the exponential convergence of several existing state-of-the-art primal-dual algorithms for solving distributed optimization without strong convexity. Finally, we provide some experiments to demonstrate the effectiveness of our results.

关键词： Convergence optimization Standards Optimized production technology Learning systems Convex functions Trajectory distributed optimization exponential convergence primal-dual methods

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Online distributed optimization with stochastic gradients:high probability bound of regrets

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Control Theory and Technology 2024年第3期22卷 419-430页

作者： Yuchen Yang Kaihong Lu Long Wang Center for Systems and Control College of EngineeringPeking UniversityBeijing 100871China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590ShandongChina

In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of *** agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a *** handle this problem,an online distributed stochastic mirror descent algorithm is *** works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the *** from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's *** mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time ***,a simulation is provided to demonstrate the effectiveness of our theoretical results.

关键词： distributed optimization Online optimization Stochastic gradient High probability

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A New Regularized Consensus Perspective for distributed optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第9期69卷 6301-6308页

作者： Ye, Maojiao Ding, Lei Xu, Shengyuan Shi, Jun Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China Nanjing Univ Posts & Telecommun Inst Adv Technol Nanjing 210023 Peoples R China

In this article, a new regularized consensus perspective is presented for solving distributed optimization problems among a network of heterogeneous linear dynamic agents. The distributed optimization problem can be viewed as a consensus problem, in which the consensus direction should be regularized to optimize the sum of the agents' objective functions. Based on this idea, a regularized consensus mapping is defined, by which a continuous-time distributed optimization algorithm is established and analyzed for heterogeneous linear dynamic agents. It is shown that the outputs of the linear dynamic agents can evolve to the distributed optimization solution. Moreover, a dynamic event-triggered scheme is proposed to achieve communication-efficient distributed optimization by reducing the communication costs among neighboring agents. Numerical simulation examples are provided to verify the effectiveness of the proposed methods.

关键词： optimization Heuristic algorithms Linear programming Vectors Manganese Vehicle dynamics Dynamical systems Communication-efficient scheme distributed optimization linear dynamic agents regularized consensus

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Community-based transactive energy market concept for 5th generation district heating and cooling through distributed optimization

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APPLIED ENERGY 2024年 371卷

作者： Qin, Qiwei Gosselin, Louis Univ Laval Dept Mech Engn Quebec City PQ Canada

Fifth -generation district heating and cooling (5GDHC) is an emerging concept that exploits heat sharing among prosumers through a low -temperature bidirectional loop. Coordinating the energy interactions in such a system is a complex problem, typically solved through centralized optimization. In addition to privacy issues for prosumers, centralized optimization can prove too hard to solve for large 5GDHC systems and cannot establish a profit distribution between prosumers. To overcome these drawbacks, this paper develops a community -based transactive energy market framework based on distributed optimization of 5GDHC. The optimization is based on the Jacobi -proximal alternating direction method of multipliers. The approach relies on iterative interactions between the network coordinator and the prosumers, the former adjusting the internal price of thermal energy and the latter adapting their heating and cooling demand. A series of test -case 5GDHC networks involving houses, commercial buildings, data centers and central boilers and chillers were numerically simulated to demonstrate how the proposed framework performs, under three electricity tariff structures (constant, time -ofuse or pay for peak). Results show that, for the cases tested, the gap between the proposed approach and global optimization is below 5% and that electricity savings compared to a situation without 5GDHC could reach 40%. The proposed method allowed to dynamically adjust the internal price of thermal energy and the prosumers ' demand while considering their thermal dissatisfaction. By facilitating 5GDHC operation, this work could help their practical implementation in the future.

关键词： Bidirectional low-temperature district energy system Demand-side management distributed optimization Jacobi-proximal ADMM Community-based market

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A Specified-Time Convergent Multiagent System for distributed optimization With a Time-Varying Objective Function

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第2期69卷 1257-1264页

作者： Zheng, Yanling Liu, Qingshan Wang, Jun Southeast Univ Sch Math Nanjing 210096 Peoples R China Southeast Univ Frontiers Sci Ctr Mobile Informat Commun & Secur Sch Math Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China City Univ Hong Kong Sch Data Sci Hong Kong Peoples R China

This technical note presents a specified-time convergent multiagent system for distributed optimization with a time-varying objective function subject to equality constraints. Different from the static optimal solutions to most existing distributed optimization problems, the optimal solutions are time varying due to the time-varying objective function in this problem. A distributed protocol law is designed to ensure all the agents' convergence to feasible and suboptimal solutions within a specified settling time and keep tracking the time-dependent optimal solutions. The specified-time convergence of the system and the asymptotic optimality of the solution generated by the system are proved based on the Lyapunov theory. A salient feature of the multiagent system is that its upper bound of settling time can be specified in advance. Two examples are presented to illustrate the theoretical results.

关键词： distributed optimization multiagent system specified-time convergence time-varying objective function

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Event-Triggered Resilient Strategy for distributed optimization With Unreliable Agents

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2024年第1期11卷 913-925页

作者： Chen, Zhao Nian, Xiaohong Meng, Qing Cent South Univ Sch Automat Changsha 410075 Peoples R China

In this article, we investigate the distributed optimization problem in the presence of unreliable agents who transmit unfavorable state information to their neighbors, resulting in misbehavior among cooperative agents. This gives rise to untrustworthy interactive information between agents. To overcome this challenge, we propose observer-based and sample-and-hold-based event-triggered resilient optimization strategies, complemented by threshold-based detection and isolation strategies. These strategies enhance the system's robustness against unreliable agents and enable cooperative agents to identify and disregard interaction information from unreliable neighbors. The system exhibits right-discontinuity due to intermittently changing communication networks and event-triggered time sequences. To analyze the convergence of nonsmooth systems, we integrate Filippov's differential inclusions with Lyapunov stability theory. Finally, we validate the efficacy of the proposed algorithms through comprehensive simulation results.

关键词： Cost function Convergence Communication networks Approximation algorithms Topology Robustness Heuristic algorithms distributed optimization unreliable agents resilient optimization strategy event-triggered

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Safety-Certified Multi-Target Circumnavigation With Autonomous Surface Vehicles via Neurodynamics-Driven distributed optimization

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2024年第4期54卷 2092-2103页

作者： Jiang, Yue Peng, Zhouhua Wang, Jun Dalian Maritime Univ Sch Marine Elect Engn Dalian 116026 Peoples R China Peking Univ Coll Engn Dept Mech & Engn Sci State Key Lab Turbulence & Complex Syst Beijing 100871 Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China City Univ Hong Kong Sch Data Sci Hong Kong Peoples R China

This article addresses multitarget circumnavigation with autonomous surface vehicles (ASVs) subject to model nonlinearities, environmental disturbances, and physical constraints in the presence of stationary/moving obstacles. A neurodynamics-driven distributed optimization method is proposed to achieve safety-certified cooperative circumnavigation guided by multiple targets. Specifically, a cooperative circumnavigation guidance law based on a finite-time distributed observer is designed for surrounding multiple targets. Based on the geometric characteristics of multitarget circumnavigation, three collision-avoidance rules are formulated with respect to obstacles, targets, and ASVs;and three types of control barrier functions are derived to encode the coupled safety constraints into state constraints. A distributed command governor optimization problem is formulated to generate optimal commanded guidance signals within the globally coupled state constraints. To compute optimal commands in real time, multiple recurrent neural networks (RNNs) are employed to solve a distributed optimization problem. An event-triggered communication scheme is designed for the communication among RNNs with reduced communication burden. A predictor-based fuzzy control law is designed to track safe velocity commands. The closed-loop system is proven to be input-to-state stable. Simulation results are elaborated to demonstrate the effectiveness of the safety-certified control method for ASVs to circumnavigate multiple targets with guaranteed safety.

关键词： Autonomous surface vehicles (ASVs) control barrier functions (CBFs) distributed optimization event-triggered communication multitarget circumnavigation neurodynamic optimization

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Consensus and Clustering Approach for Dynamic Event-Triggered distributed optimization of Power System Networks With Saturation Constraint

IEEE CANADIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING

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IEEE CANADIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING 2024年第3期47卷 136-147页

作者： Ahmed, Ijaz Rehan, Muhammad Basit, Abdul Al-Ismail, Fahad Saleh Khalid, Muhammad Pakistan Inst Engn & Appl Sci PIEAS Dept Elect Engn Islamabad 45650 Pakistan King Fahd Univ Petr & Minerals KFUPM Elect Engn Dept Dhahran 31261 Saudi Arabia King Fahd Univ Petr & Minerals KFUPM Interdisciplinary Res Ctr Sustainable Energy Syst Dhahran 31261 Saudi Arabia

This study presents a novel approach for solving the economic dispatch (ED) problem in groups of generating units communicating through a communication network. The suggested strategy is a consensus-based dynamic event-triggered (ET) distributed optimization method. Our methodology considers the sharing of the local information between generators and their convex cost functions to address the total cost function and offers a decentralized optimization solution over a network. The proposed distributed method addresses the ED problem by considering the criterion of optimal cost and by offering efficient communication. Generating units are grouped according to their generation operational limits, that is, total capacity and dynamic ET distributed protocols are developed to ensure the consensus of cost variables among generating units, operating under normal capacity conditions. The remaining generating agents work on their operating limits, which are segregated through the sharing of flag information through a switching mechanism. Consequently, in contrast to the existing methods, the recommended protocol allows nodes to function in groups, based on the power supply, for ED with geographical clustering and capacity restrictions, in addition to handling the system constraints. Furthermore, the proposed technique employs a dynamic triggering method to manage bandwidth and guarantee the elimination of Zeno behavior. The simulation results validate the efficacy of the proposed approach.

关键词： optimization Production Generators Costs Protocols Power system dynamics Cost function Consensus control distributed generation distributed optimization economic dispatch (ED) problem graph theory optimal control

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Accelerated AB/Push-Pull Methods for distributed optimization Over Time-Varying Directed Networks

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2024年第3期11卷 1395-1407页

作者： Nguyen, Duong Thuy Anh Nguyen, Duong Tung Nedic, Angelia Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ 85281 USA

This article investigates a novel approach for solving the distributed optimization problem, in which multiple agents collaborate to find the global decision that minimizes the sum of their individual cost functions. First, the AB/push-pull (ABPP) gradient-based algorithm is considered, which employs row- and column-stochastic weights simultaneously to track the optimal decision and the gradient of the global cost function, ensuring consensus on the optimal decision. Building on this algorithm, we then develop a general algorithm that incorporates acceleration techniques, such as heavy-ball momentum and Nesterov momentum, as well as their combination with nonidentical momentum parameters. Previous literature has established the effectiveness of acceleration methods for various gradient-based distributed algorithms and demonstrated linear convergence for static directed communication networks. In contrast, we focus on time-varying directed communication networks and establish the linear convergence of the methods to the optimal solution, when the agents' cost functions are smooth and strongly convex. In addition, we provide explicit bounds for the step-size value and momentum parameters, based on the properties of the cost functions, the mixing matrices, and the graph connectivity structures. Our numerical results illustrate the benefits of the proposed acceleration techniques on the ABPP algorithm.

关键词： Convergence Cost function Directed graphs Communication networks Estimation Network systems Control systems Accelerated algorithm directed graph distributed optimization time-varying graph

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