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Privacy-Preserving distributed optimization for Economic Dispatch Over Balanced Directed Networks

IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2025年 20卷 1362-1373页

作者： An, Wenjing Ding, Derui Dong, Hongli Shen, Bo Sun, Lei Univ Shanghai Sci & Technol Dept Control Sci & Engn Shanghai 200093 Peoples R China Swinburne Univ Technol Sch Sci Comp & Engn Technol Melbourne Vic 3122 Australia Northeast Petr Univ Sanya Offshore Oil & Gas Res Inst Sanya 572024 Peoples R China Northeast Petr Univ Artificial Intelligence Energy Res Inst Daqing 163318 Peoples R China Northeast Petr Univ Heilongjiang Prov Key Lab Networking & Intelligen Daqing 163318 Peoples R China Donghua Univ Coll Informat Sci & Technol Shanghai 201620 Peoples R China

Economic dispatch problems (EDPs), as a basic issue of smart grids, have appealed to a wide range of research interests owing to the expansion of network scales and the increase of system complexity. The flexibility of economic dispatch algorithms puts forward urgent requirements of distributed optimization methods dependent on information exchanges, which may lead to the leakage of private information. To solve this problem, a privacy-preserving strategy in a distributed paradigm is proposed by adding artificial sequences to the transmitted multi-step gradient information. In light of such a strategy, a new distributed privacy-preserving optimization approach in light of multi-step gradient information is developed to handle the addressed EDPs. When introduced parameter sequences satisfy suitable conditions, both the convergence to the optimal solution and the privacy of sensitive parameters in the generator cost are effectively guaranteed. Finally, an illustrative simulation is specially offered to verify the validity of the developed strategy.

关键词： Economic dispatch privacy-preserving distributed optimization multi-step gradient smart grids

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A unified combination scheme for online learning and distributed optimization over networks ☆

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DIGITAL SIGNAL PROCESSING 2025年 159卷

作者： Jin, Danqi Chen, Yitong Chen, Jie Huang, Gongping Wuhan Univ Sch Elect Informat Wuhan Peoples R China Northwestern Polytech Univ Ctr Intelligent Acoust & Immers Commun Sch Marine Sci & Technol Xian Peoples R China

Both convex and affine combinations are highly effective for distributed adaptive networks, enabling these networks to create new diffusion strategies by combining the strengths of candidate diffusion strategies. However, these schemes are typically designed for mean-square error costs and linear models, and all nodes in a network are constrained to use the same scheme. To overcome the limitations of current combination schemes, we propose a novel unified combination scheme that accommodates possibly nonlinear models and general convex cost functions. This scheme also unifies convex and affine combination schemes, allowing nodes within the same network to have different choices. Our unified scheme is flexible enough to accommodate an arbitrary number of candidate algorithms, and allows for the independent and flexible setting of criteria for deriving each candidate algorithm as well as for the combination layer. To further enhance its performance, we introduce a weight-transfer trick among multiple candidate strategies. Finally, simulation results validate the effectiveness of our proposed scheme and provide guidance on the selection of its step-size parameter.

关键词： distributed optimization Online learning Diffusion strategy Unified combination scheme General cost function

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Linear Convergence of Asynchronous Gradient Push Algorithm for distributed optimization

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第3期55卷 2147-2159页

作者： Li, Huaqing Cheng, Huqiang Lu, Qingguo Wang, Zheng Huang, Tingwen Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Chongqing Univ Key Lab Dependable Serv Comp Cyber Phys Soc Minist Educ Chongqing 400044 Peoples R China Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China Shenzhen Univ Adv Technol Fac Comp Sci & Control Engn Shenzhen 518055 Peoples R China

This article focuses on multiagent distributed asynchronous optimization over directed networks where each agent can only access its individual local function, and the aggregate aim is to minimize the cumulative sum of all local functions. Considering the asynchrony among the agents, we develop an algorithm in which agents compute and communicate individually, without any form of synchronized coordination. Agents perform their local updates by local communication with their immediate neighbors, and this may involve the use of stale information. Since asynchrony naturally leads to latency or packet loss, an asynchronous robust gradient tracking mechanism is developed to guarantee estimating the average of agents' gradients precisely. Moreover, it employs uncoordinated step-sizes which are more flexible and general than constant or decaying step-size. When the global objective is strongly convex and the local objectives have Lipschitz-continuous gradients, we prove that each agent executing the asynchronous algorithm linearly converges to the consensus optimal point at an O(lambda(k)) rate, where lambda is an element of (0, 1) is convergence factor and k represents the iteration number, with a step satisfying a tight explicit upper bound. Numerical experiments demonstrate that our algorithm has better advantages over the state-of-the-art asynchronous algorithms.

关键词： Convergence optimization Protocols System recovery Linear programming Electronic mail Delays Vectors Synchronization Fasteners Asynchronous algorithm delay distributed optimization linear convergence

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ON THE GEOMETRIC CONVERGENCE OF BYZANTINE-RESILIENT distributed optimization ALGORITHMS

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SIAM JOURNAL ON optimization 2025年第1期35卷 210-239页

作者： Kuwaranancharoen, Kananart Sundaram, Shreyas Purdue Univ Elmore Family Sch Elect & Comp Engn W Lafayette IN 47907 USA

The problem of designing distributed optimization algorithms that are resilient to Byzantine adversaries has received significant attention. For the Byzantine-resilient distributed optimization problem, the goal is to (approximately) minimize the average of the local cost functions held by the regular (nonadversarial) agents in the network. In this paper, we provide a general algorithmic framework for Byzantine-resilient distributed optimization which includes some state-of-the-art algorithms as special cases. We analyze the convergence of algorithms within the framework, and derive a geometric rate of convergence of all regular agents to a ball around the optimal solution (whose size we characterize). Furthermore, we show that approximate consensus can be achieved geometrically fast under some minimal conditions. Our analysis provides insights into the relationship among the convergence region, distance between regular agents' values, step size, and properties of the agents' functions for Byzantine-resilient distributed optimization.

关键词： consensus algorithm convex optimization distributed algorithms distributed optimization fault tolerant systems linear convergence multiagent systems network security

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Differentially Private Dynamic Average Consensus-Based Newton Method for distributed optimization Over General Networks

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第2期55卷 1348-1361页

作者： Xing, Mingqi Ma, Dazhong Zhao, Jing Wong, Pak Kin Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Univ Macau Dept Electromech Engn Macau Peoples R China

This article investigates the issue of privacy preservation in distributed optimization, where each node possesses a local private objective function and collaborates to minimize the sum of those functions. A novel dynamic average consensus-based distributed Newton algorithm is introduced to achieve consensus, optimality, and differential privacy. Each node utilizes its local gradient and Hessian as time-varying reference signals, facilitating information exchange with neighbors for tracking the average. To safeguard privacy, persistent Laplace noise is introduced into the exchanged data, affecting the estimated optimal solution, gradient, and Hessian averages. To counteract the noise's impact, the internode coupling strength is adaptively reduced over time through decay factors, allowing for noise attenuation as the algorithm progresses. The algorithm's convergence to the optimal solution, assuming global function smoothness and strong convexity, is theoretically proven. The algorithm's accurate convergence to the optimal solution, assuming global function smoothness and strong convexity, is theoretically proven. Furthermore, the efficiency and reliability of the algorithm are empirically validated through simulations of an IEEE 14-bus test system.

关键词： Newton method Differential privacy distributed optimization distributed optimization dynamic average consensus dynamic average consensus unbalanced directed graph unbalanced directed graph unbalanced directed graph

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Event-triggered predefined-time distributed optimization algorithm based on zero-gradient-sum

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SYSTEMS & CONTROL LETTERS 2025年 196卷

作者： Guo, Ge Zhang, Xinxin Zhang, Renyongkang Kang, Jian Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China Northeastern Univ Qinhuangdao Sch Control & Engn Qinhuangdao 066004 Peoples R China Dalian Maritime Univ Coll Marine Elect Engn Dalian 116026 Peoples R China

This paper presents an event-triggered distributed optimization (DO) algorithm for consensus constraints and strongly convex local cost functions. The algorithm is derived by means of the zero-gradient-sum mechanism and sliding mode control, which is free from any initial conditions or local minimization. In order to avoid continuous communication and measurement, our algorithm enables the interaction between agents solely at event-triggered instants, resulting in conserving communication resources. Importantly, the proposed method drives system to the optimal consensus state within a predefined time. Simulation results demonstrate the effectiveness of our approach.

关键词： distributed optimization Event-trigger Predefined-time convergence Multi-agent systems

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A Tutorial on distributed optimization for Cooperative Robotics: From Setups and Algorithms to Toolboxes and Research Directions

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PROCEEDINGS OF THE IEEE 2025年第1期113卷 40-65页

作者： Testa, Andrea Carnevale, Guido Notarstefano, Giuseppe Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy

Several interesting problems in multirobot systems can be cast in the framework of distributed optimization. Examples include multirobot task allocation, vehicle routing, target protection, and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this article, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss its implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots.

关键词： optimization Robots Multi-robot systems Robot kinematics Surveillance Resource management distributed algorithms Tutorials Formation control Vehicle routing Cooperating robots distributed optimization distributed robot systems optimization and optimal control

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A Row-Stochastic Event-Based Quantized Algorithm for distributed optimization With Linear Convergence

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第6期55卷 2937-2948页

作者： Xing, Mingqi Ma, Dazhong Zhang, Huaguang Zhao, Jing Wong, Pak Kin Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Univ Macau Dept Electromech Engn Macau Peoples R China

This article proposes the row-stochastic event-based quantized (RSEQ) algorithm to address the distributed optimization problem with multiple communication constraints, including limited communication costs and bandwidth. In RSEQ, a novel event-based dynamic quantizer is designed to resist the negative effects of communication constraints on the algorithm. The quantizer encompasses the event generator and the dynamic encoder/decoder, which collectively adapt the frequency and size of information sharing based on real-time state. The RSEQ only requires the construction of a row-stochastic weight matrix, which leads to lower conservatism compared to algorithms based on column-stochastic matrices. Additionally, the introduction of an acceleration term enables RSEQ to linearly converge to the globally optimal solution without the deployment of the average gradient estimator. Instead, a Perron vector estimator needs to be employed to counteract the unbalancedness of the directed network. With the effect of the event generator, the Perron vector estimator can also be left inactive after a certain number of iterations, which means that the transmission of only state information between agents can linearly converge to the global optimal solution under directed networks. Finally, the effectiveness of the algorithm is demonstrated through an economic dispatch problem in smart grids.

关键词： Event detection Vectors Heuristic algorithms Convergence Bandwidth Costs Quantization (signal) Linear programming Directed graphs Cost function distributed optimization linear convergence quantized communication row-stochastic weight

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THE DESIGN OF CONTINUOUS-TIME ACCELERATED ALGORITHM FOR NONSMOOTH distributed optimization WITHOUT SHARING LOCAL DECISION VARIABLES

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JOURNAL OF INDUSTRIAL AND MANAGEMENT optimization 2025年第3期21卷 1867-1896页

作者： Yuan, Xiaolan Wu, Xiang Guizhou Normal Univ Sch Math Sci Guiyang 550025 Peoples R China

This paper proposes an accelerated strategy aimed at safeguarding the privacy of the multi-agent system (MAS) and enhancing the optimization algorithm's convergence rate. First of all, a local penalty factor and an auxiliary variable are introduced to reformulate the original distributed optimization (DO) problem, which involves a nonsmooth objective function and set constraints. To the best of our understanding, this is the first exploration in DO to introduce the concept of the local penalty factor. Subsequently, we use Nesterov's accelerated approach to develop a distributed continuous-time primal-dual accelerated algorithm while guaranteeing that local decision variables are not shared. It is demonstrated that this algorithm is convergent and can achieve a convergence rate of O(1/t(2)). In conclusion, the superiority and effectiveness of the mentioned strategy are substantiated by three numerical simulations.

关键词： Multi-agent system distributed optimization continuous-time algorithm Nesterov's accelerated approach nonsmooth function

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A real-time distributed optimization control for power sharing and voltage restoration in inverter-based microgrids

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AIN SHAMS ENGINEERING JOURNAL 2025年第2期16卷

作者： Khan, Asad Khan, Muhammad Mansoor Chuanwen, Jiang Khan, Danish Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Key Lab Control Power Transmiss & Transformat Minist Educ Shanghai 200240 Peoples R China Zhejiang Univ Sch Elect Engn Hangzhou 310027 Peoples R China

This paper presents a distributed control framework for grid-forming (GFM) distributed generations (DGs), considering the objectives of active/reactive power sharing and load feeder voltage regulation in inverter-based microgrids (MGs). Battery energy storage systems (BESSs) are controlled GFM sources while solar-powered DGs are working in grid-following (GFL) mode to provide active power support. The proposed method simplifies the global optimization problem into multiple sub-optimal problems by virtually segregating each GFM source into two decoupled sources. Each sub-problem, containing at most two GFM sources and multiple GFL sources with a single distributed agent, is solvable independently using local and neighboring node information. This feature substantially minimizes computational and communication resources, allowing for solutions using low-cost digital signal processors (DSPs). Moreover, the highly distributed nature of the proposed search algorithm ensures fast solution convergence and real-time implementation in multi-agent systems (MAS). Compared to existing segregation methods like Alternating Direction Method of Multipliers (ADMM) and Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) schemes, which segregate the network into complex sub-networks involving several GFM sources, the proposed approach is more suitable for small-scale inverter-based MGs. The framework's effectiveness is validated through analytical formulation, MATLAB simulations, and realistic experimental results within a multi-feeder test MG system, which includes numerous load feeders and sparsely available GFM DGs, a scenario that has received limited attention in existing literature.

关键词： Multi-feeder microgrids distributed optimization Power sharing Voltage regulation Decoupled spherical search method battery-powered grid-forming DGs solar-powered grid-following DGs

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