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EFIX: Exact fixed point methods for distributed optimization

JOURNAL OF GLOBAL optimization 2023年第3期85卷 637-661页

作者： Jakovetic, Dusan Krejic, Natasa Jerinkic, Natasa Krklec Univ Novi Sad Fac Sci Novi Sad Serbia

We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use the standard reformulation-transforming the original problem into a constrained problem in a higher dimensional space-to define a sequence of suitable quadratic penalty subproblems with increasing penalty parameters. For quadratic objectives, the corresponding sequence consists of quadratic penalty subproblems. For generic strongly convex case, the objective function is approximated with a quadratic model and hence the sequence of the resulting penalty subproblems is again quadratic. EFIX is then derived by solving each of the quadratic penalty subproblems via a fixed point (R)-linear solver, e.g., Jacobi Over-Relaxation method. The exact convergence is proved as well as the worst case complexity of order O(epsilon(-1)) for the quadratic case. In the case of strongly convex generic functions, the standard result for penalty methods is obtained. Numerical results indicate that the method is highly competitive with state-of-the-art exact first order methods, requires smaller computational and communication effort, and is robust to the choice of algorithm parameters.

关键词： Fixed point methods Quadratic penalty method distributed optimization Strongly convex problems

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Predefined-Time Formation Control for Multiagent Systems-Based on distributed optimization

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第12期53卷 7980-7988页

作者： Villeros, Pablo De Sanchez-Torres, Juan Diego Defoort, Michael Djemai, Mohamed Loukianov, Alexander Polytech Hauts Defrance LAMIH UMR CNRS 8201 F-59313 Valenciennes France Dept Elect Engn Zapopan 45017 Mexico ITESO Dept Math & Phys Santa Mara Tequepexpan 45604 Mexico Univ Polytech Hauts Defrance LAMIH UMR CNRS 8201 F-59313 Valenciennes France QUARTZ Lab EA 7393 ENSEA F-95000 Cergy France Dept Elect Engn Zapopan 45017 Mexico

This article presents a solution to the leaderless formation control problem for first-order multiagent systems, which minimizes a global function composed of a sum of local strongly convex functions for each agent under weighted undirected graphs within a predefined time. The proposed distributed optimization process consists of two steps: 1) the controller initially leads each agent to the minimizer of its local function and 2) then guides all agents toward achieving leaderless formation and reaching the global function's minimizer. The proposed scheme requires fewer adjustable parameters than most existing methods in the literature without the need for auxiliary variables or time-variable gains. Additionally, one can consider highly nonlinear multivalued strongly convex cost functions, while the agents do not share the gradients and Hessians. Extensive simulations and comparisons with state-of-the-art algorithms demonstrate the effectiveness of our approach.

关键词： Power system stability Formation control Cost function Asymptotic stability Task analysis Robot sensing systems Numerical stability distributed optimization fixed-time stability formation control multiagent systems predefined-time stability

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Accelerating distributed optimization via Over-the-Air Computing

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IEEE TRANSACTIONS ON COMMUNICATIONS 2023年第9期71卷 5565-5579页

作者： Mitsiou, Nikos A. Bouzinis, Pavlos S. Diamantoulakis, Panagiotis D. Schober, Robert Karagiannidis, George K. Aristotle Univ Thessaloniki Dept Elect & Comp Engn Wireless Commun & Informat Proc WCIP Grp Thessaloniki 54636 Greece Friedrich Alexander Univ Erlangen Nurnberg FAU Inst Digital Commun D-91058 Erlangen Germany Lebanese Amer Univ LAU Cyber Secur Syst & Appl AI Res Ctr Beirut 11022801 Lebanon

distributed optimization is ubiquitous in emerging applications, such as robust sensor network control, smart grid management, machine learning, resource slicing, and localization. However, the extensive data exchange among local and central nodes may cause a severe communication bottleneck. To overcome this challenge, over-the-air computing (AirComp) is a promising medium access technology, which exploits the superposition property of the wireless multiple access channel (MAC) and offers significant bandwidth savings. In this work, we propose an AirComp framework for general distributed convex optimization problems. Specifically, a distributed primal-dual (DPD) subgradient method is utilized for the optimization procedure. Under general assumptions, we prove that DPD-AirComp can asymptotically achieve zero expected constraint violation. Therefore, DPD-AirComp ensures the feasibility of the original problem, despite the presence of channel fading and additive noise. Moreover, with proper power control of the users' signals, the expected non-zero optimality gap can also be mitigated. Two practical applications of the proposed framework are presented, namely, smart grid management and wireless resource allocation. Finally, numerical results confirm DPD-AirComp's excellent performance, while it is also shown that DPD-AirComp converges an order of magnitude faster compared to two digital orthogonal multiple access schemes, specifically, time-division multiple access (TDMA), and orthogonal frequency-division multiple access (OFDMA).

关键词： optimization Convergence Smart grids Servers Resource management Linear programming 6G mobile communication Over-the-air computing non-orthogonal multiple access primal-dual distributed optimization subgradient method 6G large-scale optimization

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Privacy-Preserved distributed optimization for Multi-Agent Systems With Antagonistic Interactions

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2023年第3期70卷 1350-1360页

作者： Luo, Qi Liu, Shuai Wang, Licheng Tian, Engang Univ Shanghai Sci & Technol Coll Sci Shanghai 200093 Peoples R China Shanghai Univ Elect Power Coll Automat Engn Shanghai 200090 Peoples R China Univ Shanghai Sci & Technol Sch Opt Elect & Comp Engn Shanghai 200093 Peoples R China

This paper is concerned with the privacy-preserving distributed optimization problem for a class of cooperative-competitive multi-agent systems. Each agent only knows its own local objective function and interacts the state information with neighbors through a communication network. By means of the signed graph theory, the antagonistic interactions among agents are considered to characterize both the cooperative and the competitive relationships. With the help of the gauge transformation technique, a structurally balanced undirected signed graph is firstly transformed into a standard undirected graph. Then, the distributed optimization problem subject to signed network is converted into the traditional distributed optimization problem. Subsequently, a novel privacy-preserving distributed optimization algorithm is put forward to 1) minimize the sum of local objective functions;2) achieve the bipartite consensus for all agents;and 3) avoid the information leakage caused by message exchange among agents, simultaneously. Finally, a simulation example is given to verify the effectiveness of the proposed optimization algorithm.

关键词： distributed optimization multi-agent systems differential privacy bipartite consensus signed graph

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Differentially Private distributed optimization With an Event-Triggered Mechanism

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2023年第7期70卷 2943-2956页

作者： Mao, Shuai Yang, Minglei Yang, Wen Tang, Yang Zheng, Wei Xing Gu, Juping Werner, Herbert Nantong Univ Dept Elect Engn Nantong 226019 Peoples R China East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China Western Sydney Univ Sch Comp Data & Math Sci Sydney NSW 2751 Australia Hamburg Univ Technol Inst Control Syst D-21073 Hamburg Germany

This study concentrates on the differential private distributed optimization problem with an event-triggered mechanism, whose goals include preserving the privacy of agents' initial states and local cost functions and improving communication efficiency. A distributed event-triggered mechanism is integrated into the differentially private subgradient-push distributed optimization algorithm and then a new algorithm named as DP-ETSP is designed, where the real-time information propagation among agents is avoided. Additionally, under the proposed event-triggered mechanism, an analysis of mean-square consensus and optimality over time-varying directed networks is made when the added Laplace noises meet some specific decaying conditions. Convergence rate results are further established under a specific stepsize, which are equal to the rate of stochastic gradient-push algorithm without event-triggered communication. Moreover, the differential privacy preservation performance is analyzed and the rule for selecting privacy level is discussed. Finally, the feasibility and effectiveness of DP-ETSP are verified in two simulation cases.

关键词： distributed optimization event-triggered mechanism differential privacy

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distributed optimization under edge agreements: A continuous-time algorithm

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SYSTEMS & CONTROL LETTERS 2024年 183卷

作者： Lu, Zehui Mou, Shaoshuai Purdue Univ Sch Aeronaut & Astronaut 701 W Stadium Ave W Lafayette IN 47907 USA

Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge agreements are defined locally to allow more flexibility than a global consensus. This work formulates a multi-agent optimization problem under edge agreements and proposes a continuous-time distributed algorithm to solve it. Both analytical proof and numerical examples are provided to validate the effectiveness of the proposed algorithm.

关键词： Multi-agent systems distributed optimization Edge agreements

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Event-triggered distributed optimization of multi-agent systems with time delay

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2023年第12期20卷 20712-20726页

作者： Tang, Run Zhu, Wei Pu, Huizhu Chongqing Univ Posts & Telecommun Key Lab Intelligent Anal & Decis Complex Syst Chongqing 400065 Peoples R China

In this article, the distributed optimization based on multi-agent systems was studied, where the global optimization objective of the optimization problem is a convex combination of local objective functions. In order to avoid continuous communication among neighboring agents, an event triggering algorithm was proposed. Time delay was also considered in the designed algorithm. The triggering time of each agent was determined by the state measurement error, the state of its neighbors at the latest triggering instant and the exponential decay threshold. Some sufficient conditions for optimal consistency were obtained. In addition, Zeno-behavior in triggering time sequence was eliminated. Finally, a numerical simulation was given to prove the effectiveness of the proposed algorithm.

关键词： multi-agent systems event-triggered distributed optimization time delay

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OPTIMAL METHODS FOR CONVEX RISK-AVERSE distributed optimization

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SIAM JOURNAL ON optimization 2023年第3期33卷 1518-1557页

作者： Lan, Guanghui Zhang, Zhe Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

This paper studies the communication complexity of convex risk-averse optimization over a network. The problem generalizes the well-studied risk-neutral finite-sum distributed optimization problem, and its importance stems from the need to handle risk in an uncertain environment. For algorithms in the literature, a gap exists in communication complexities for solving risk-averse and risk-neutral problems. We propose two distributed algorithms, namely the distributed risk-averse optimization (DRAO) method and the distributed risk-averse optimization with sliding (DRAO-S) method, to close the gap. Specifically, the DRAO method achieves optimal communication complexity by assuming a certain saddle point subproblem can be easily solved in the server node. The DRAO-S method removes the strong assumption by introducing a novel saddle point sliding subroutine which only requires the projection over the ambiguity set P. We observe that the number of P-projections performed by DRAO-S is optimal. Moreover, we develop matching lower complexity bounds to show the communication complexities of both DRAO and DRAO-S to be unimprovable. Numerical experiments are conducted to demonstrate the encouraging empirical performance of the DRAO-S method.

关键词： risk-averse optimization distributed optimization first-order algorithm convex optimization lower complexity

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Fuzzy Small-Gain Approach for the distributed optimization of T-S Fuzzy Cyber-Physical Systems

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第10期53卷 6491-6502页

作者： Jin, Zhenghong Sun, Xingjian Qin, Zhengyan Ahn, Choon Ki Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Nantong Univ Sch Elect Engn Nantong 226019 Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China Korea Univ Sch Elect Engn Seoul 136701 South Korea

The distributed optimization problem (DOP) of Takagi-Sugeno (T-S) fuzzy cyber-physical systems is studied under the framework of weight-balanced graphs and quasistrongly connected characteristics. The objective is to drive the outputs of all agents to the optimal solution of a given global objective function regarded as the desired output, based on the partial information of the local objective functions. To this end, distributed optimal coordinators (DOCs) are used to generate optimal solutions of local objective functions that converge to the desired output, and fuzzy reference-tracking controllers are designed to ensure that all agents can track the optimal solutions. As novel technical results, two Lyapunov-based fuzzy input-to-state stability (ISS) small-gain theorems are proposed for the T-S fuzzy interconnected system. Thus, the overall closed-loop system is an interconnected system involving the modules of optimal coordinators and fuzzy tracking controllers with T-S fuzzy subsystems. The fuzzy ISS cyclic-small-gain theorem is applied to analyze the system stability. The DOP of T-S fuzzy cyber-physical systems is solved using the DOCs and fuzzy reference-tracking controllers through the fuzzy small-gain approach. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed method.

关键词： optimization Linear programming Interconnected systems Heuristic algorithms Topology Stability criteria Convergence distributed optimization fuzzy input-to-state stability (ISS) cyclic-small-gain theorem fuzzy reference-tracking controllers Takagi-Sugeno (T-S) fuzzy cyber-physical systems

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A Bi-Event-Triggered Multi-Agent System for distributed optimization

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2023年第2期10卷 1074-1084页

作者： Huang, Banghua Liu, Yang Xia, Zicong Wang, Jun Zhejiang Normal Univ Coll Math & Comp Sci Jinhua 321004 Peoples R China Zhejiang Normal Univ Coll Math & Comp Sci Key Lab Intelligent Educ Technol & Applicat Zhejia Jinhua 321004 Peoples R China Linyi Univ Sch Automat & Elect Engn Linyi 276005 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

In this paper, we propose a continuous-time multi-agent system via event-triggered communication among agents for distributed optimization. We develop a dynamic bi-event triggering rule based on both local decision variables and auxiliary variables to reduce communication costs. We design a bi-event triggered multi-agent system based on the Karush-Kuhn-Tucker conditions, which allows initializing auxiliary variables arbitrarily and hence relaxing the existing zero-sum condition on the initial values of auxiliary variables. We prove the exponential convergence of the multi-agent system to the optimal solution and derive a lower bound of the convergence rate. In addition, we prove the capability of the triggering rule for precluding Zeno behavior. We also elaborate on two numerical examples to illustrate the effectiveness and characteristics of the theoretical results.

关键词： optimization Linear programming Eigenvalues and eigenfunctions Bandwidth Convergence Behavioral sciences Protocols distributed optimization event-triggered communication multi-agent systems Zeno behavior

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