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Extended Zero-Gradient-Sum Approach for constrained distributed optimization With Free Initialization

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第6期55卷 3824-3834页

作者： Shi, Xinli Yu, Xinghuo Wen, Guanghui Xu, Xiangping Southeast Univ Sch Cyber Sci & Engn Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3001 Australia Southeast Univ Sch Automat Nanjing 210096 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China

This article proposes an extended zero-gradient-sum (EZGS) approach for solving constrained distributed optimization with free initialization and desired convergence properties. A Newton-based continuous-time algorithm is first designed for general constrained optimization, which is adapted to handle inequality constraints by using log-barrier penalty functions. Then, a general class of EZGS dynamics is developed to address equation-constrained distributed optimization, where an auxiliary dynamics is introduced to ensure the final ZGS property from any initialization. It is demonstrated that for typical consensus protocols and auxiliary dynamics, the proposed EZGS dynamics can achieve the performance with exponential/finite/fixed/prescribed-time (PT) convergence. Particularly, the nonlinear consensus protocols for finite-time EZGS algorithms allow for heterogeneous power coefficients. Significantly, the proposed PT EZGS dynamics is continuous, uniformly bounded, and capable of reaching the optimal solution in a single stage. Furthermore, the barrier method is employed to handle the inequality constraints effectively. Finally, the efficiency and performance of the proposed algorithms are validated through numerical examples, highlighting their superiority over existing methods. In particular, by selecting appropriate protocols, the proposed EZGS dynamics can achieve desired convergence performance.

关键词： optimization Convergence Heuristic algorithms Consensus protocol Estimation Couplings Resource management Classification algorithms Vehicle dynamics Vectors Barrier method constrained distributed optimization convergence rate finite-time (FT) stability zero-gradient-sum (ZGS) method

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Exponentially Convergent Algorithm Design for constrained distributed optimization via Nonsmooth Approach

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第2期67卷 934-940页

作者： Li, Weijian Zeng, Xianlin Liang, Shu Hong, Yiguang Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China Beijing Inst Technol Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Tongji Univ Dept Control Sci & Engn Shanghai 201804 Peoples R China Shanghai Res Inst Intelligent Syst Shanghai 201203 Peoples R China

We develop an exponentially convergent distributed algorithm to minimize a sum of nonsmooth cost functions with a set constraint. The set constraint generally leads to the nonlinearity in distributed algorithms, and results in difficulties to derive an exponential rate. In this article, we remove the consensus constraints by an exact penalty method, and then propose a distributed projected subgradient algorithm by virtue of a differential inclusion and a differentiated projection operator. Resorting to nonsmooth approaches, we prove the convergence for this algorithm, and moreover, provide both the sublinear and exponential rates under some mild assumptions.

关键词： Convergence distributed algorithms Cost function Heuristic algorithms Resource management Topology Intelligent control constrained distributed optimization exact penalty method exponential convergence nonsmooth approach projected gradient dynamics

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Privacy distributed constrained optimization Over Time-Varying Unbalanced Networks and Its Application in Federated Learning

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IEEE/CAA Journal of Automatica Sinica 2025年第2期12卷 335-346页

作者： Mengli Wei Wenwu Yu Duxin Chen Mingyu Kang Guang Cheng the School of Cyber Science and Engineering Southeast University IEEE the School of Mathematics Frontiers Science Center for Mobile Information Communication and Security Southeast University the Purple Mountain Laboratories the School of Mathematics Southeast University

This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced *** hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.

关键词： constrained distributed optimization decentralized federated learning (DFL) differential privacy (DP) time-varying unbalanced graphs zeroth-order gradient

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A penalty-like neurodynamic approach to constrained nonsmooth distributed convex optimization

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NEUROCOMPUTING 2020年第0期377卷 225-233页

作者： Jiang, Xinrui Qin, Sitian Xue, Xiaoping Harbin Inst Technol Dept Math Harbin 150001 Heilongjiang Peoples R China Harbin Inst Technol Dept Math Weihai 264209 Peoples R China

A nonsmooth distributed optimization problem subject to affine equality and convex inequality is considered in this paper. All the local objective functions in the distributed optimization problem possess a common decision variable. And taking privacy into consideration, each agent doesn't share its local information with other agents, including the information about the local objective function and constraint set. To cope with this distributed optimization, a neurodynamic approach based on the penalty-like methods is proposed. It is proved that the presented neurodynamic approach is convergent to an optimal solution to the considered distributed optimization problem. The proposed neurodynamic approach in this paper has lower model complexity and computational load via reducing auxiliary variables. In the end, two illustrative examples are given to show the effectiveness and practical application of the proposed neural network. (c) 2019 Elsevier B.V. All rights reserved.

关键词： constrained distributed optimization Neurodynamic approach Differential inclusion

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On the Convergence Properties of a distributed Projected Subgradient Algorithm

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第12期68卷 7546-7559页

作者： Li, Weijian Chen, Zihan Lou, Youcheng Hong, Yiguang South Univ Sci & Technol China Sch Syst Design & Intelligent Mfg Shenzhen 518055 Peoples R China Huawei Technol Co Ltd Beijing 100031 Peoples R China Chinese Acad Sci Acad Math & Syst Sci MDIS Beijing 100045 Peoples R China Tongji Univ Dept Control Sci & Engn Shanghai 200070 Peoples R China Shanghai Res Inst Intelligent Syst Shanghai 200082 Peoples R China

A weight-balanced network plays an important role in the exact convergence of a distributed optimization algorithm, but is not always satisfied in practice. Different from most of existing works focusing on designing distributed algorithms, in this article, we analyze the convergence of a well-known distributed projected subgradient algorithm over time-varying general graph sequences, i.e., the weight matrices of the network are only required to be row stochastic instead of doubly stochastic. We first show that there may exist a graph sequence such that the algorithm is not convergent when the network switches freely within finitely many graphs. Then, to guarantee its convergence under any uniformly jointly strongly connected graph sequence, we provide a necessary and sufficient condition on the cost functions, i.e., the intersection of optimal solution sets to all local optimization problems is not empty. Furthermore, we surprisingly find that the algorithm is convergent for any periodically switching graph sequence, but the converged solution minimizes a weighted sum of local cost functions, where the weights depend on the Perron vectors of some product matrices of the underlying switching graphs. Finally, we consider a slightly broader class of quasi-periodically switching graph sequences, and show that the algorithm is convergent for any quasi-periodic graph sequence if and only if the network switches between only two graphs. This work helps us understand impacts of communication networks on the convergence of distributed algorithms, and complements existing results from a different viewpoint.

关键词： Communication network constrained distributed optimization convergence analysis projected subgradient algorithm

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Continuous-Time Algorithm for Approximate distributed optimization With Affine Equality and Convex Inequality Constraints

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第9期51卷 5809-5818页

作者： Jiang, Xinrui Qin, Sitian Xue, Xiaoping Harbin Inst Technol Dept Math Harbin 150001 Peoples R China Harbin Inst Technol Dept Math Weihai 264209 Peoples R China

A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DOP (ADOP) is presented. It is proved that the optimal solutions of the ADOP (i.e., the near-optimal solutions of the original DOP) are able to approach the optimal solutions of the original DOP. A continuous-time algorithm is proposed for the ADOP and it is demonstrated that the state solution of the presented algorithm converges to the critical point set of the ADOP with general locally Lipschitz continuous objective functions. This means the presented algorithm is efficient for distributed nonconvex optimization problems. Particularly, when the objective functions are convex ones, the state solution of the presented algorithm is further proved to converge to a near-optimal solution of the original DOP. One illustrative example and an application on load sharing problems are shown to validate the effectiveness of the proposed algorithm.

关键词： optimization Directed graphs Approximation algorithms Linear programming Nickel distributed algorithms Power systems constrained distributed optimization continuous-time algorithm near-optimal solutions

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Event-Based Broadcasting for Stochastic Subgradient Algorithms 7

Event-Based Broadcasting for Stochastic Subgradient Algorith...

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7th International Conference on Event-Based Control, Communication and Signal Processing (EBCCSP)

作者： Dhullipalla, Mani H. Yu, Hao Chen, Tongwen Univ Alberta Elect & Comp Engn Edmonton AB Canada

ISBN: (纸本)9781665436977

Stochastic subgradient algorithms (SSAs) are widely studied owing to their applications in distributed and online learning. However, in a distributed setting, their sub-linear convergence rates tend to attract a large number of information exchanges that raise the overall communication burden. In order to reduce this burden, in this paper, we design two static stochastic event-based broadcasting protocols that operate in conjunction with SSAs to address a set-constrained distributed optimization problem (DOP). We address two notions of stochastic convergence, namely, almost sure and mean convergence;for each of these notions we design event-based broadcasting protocols, specifically, the stochastic event-thresholds. Subsequently, we illustrate the design via a numerical example and provide comparisons to evaluate its performance against the existing event-based protocols.

关键词： stochastic subgradient event-based broadcasting constrained distributed optimization

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A Hierarchical ADMM Based Framework for EV Charging Scheduling

A Hierarchical ADMM Based Framework for EV Charging Scheduli...

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IEEE/PES Transmission and Distribution Conference and Exposition (T and D)

作者： Khaki, Behnam Chu, Chicheng Gadh, Rajit Univ Calif Los Angeles Smart Grid Energy Res Ctr SMERC Los Angeles CA 90095 USA

ISBN: (纸本)9781538655832

Electric vehicles (EVs) are controllable loads from which distribution grid operator can benefit in order to minimize the load profile variations. In this paper, we proposed a hierarchical distributed optimization framework such that EV management system (EVMS), as a part of distribution grid management system, minimizes the load variance of the grid in communication with the EV aggregators which control EV charging load of the distribution system feeders. The hierarchical distributed framework, based on alternative direction method of multipliers (ADMM), increases the scalability of the EV charging infrastructure while decreases computational burden. In our proposed approach, each EV aggregator schedules the EV charging profiles of its feeder in a distributed fashion which avoids sharing the EV owners' desired charging profile information and enables privacy preserving. To show the performance of our approach, we apply it to a case study with 100% EV penetration, including 4 feeders and 60 EVs, and show how the load variance of the system and charging cost of individual EVs decrease.

关键词： EV charging scheduling constrained distributed optimization hierarchical ADMM

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distributed Continuous-Time Algorithm for constrained Convex optimizations via Nonsmooth Analysis Approach

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第10期62卷 5227-5233页

作者： Zeng, Xianlin Yi, Peng Hong, Yiguang Chinese Acad Sci Inst Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China Univ Toronto Dept Elect & Comp Engn Toronto ON Canada

This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost function and local constraint set, for the constrained optimization problem. Then we prove that all the agents of the algorithm can find the same optimal solution, and meanwhile, keep the states bounded while seeking the optimal solutions. We conduct a complete convergence analysis by employing nonsmooth Lyapunov functions for the stability analysis of differential inclusions. Finally, we provide a numerical example for illustration.

关键词： constrained distributed optimization continuous-time algorithms multi-agent systems nonsmooth analysis projected dynamical systems

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