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Continuous-Time distributed Subgradient Algorithm for convex optimization With General Constraints

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2019年第4期64卷 1694-1701页

作者： Zhu, Yanan Yu, Wenwu Wen, Guanghui Chen, Guanrong Ren, Wei Southeast Univ Sch Math Nanjing 210096 Jiangsu Peoples R China Nantong Univ Dept Elect Engn Nantong Peoples R China RMIT Univ Sch Engn Melbourne Vic 3001 Australia City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China Univ Calif Riverside Dept Elect & Comp Engn Riverside CA 95251 USA

The distributed convex optimization problem is studied in this paper for any fixed and connected network with general constraints. To solve such an optimization problem, a new type of continuous-time distributed subgradient optimization algorithm is proposed based on the Karuch-Kuhn-Tucker condition. By using tools from nonsmooth analysis and set-valued function theory. it is proved that the distributed convex optimization problem is solved on a network of agents equipped with the designed algorithm. For the case that the objective function is convex but not strictly convex, it is proved that the states of the agents associated with optimal variables could converge to an optimal solution of the optimization problem. For the case that the objective function is strictly convex, it is further shown that the states of agents associated with optimal variables could converge to the unique optimal solution. Finally, some simulations are performed to illustrate the theoretical analysis.

关键词： Continuous-time subgradient algorithm distributed convex optimization multiagent systems nonsmooth analysis

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Event-Triggered distributed Stochastic Mirror Descent for convex optimization

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第9期34卷 6480-6491页

作者： Xiong, Menghui Zhang, Baoyong Ho, Daniel W. C. Yuan, Deming Xu, Shengyuan Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Jiangsu Peoples R China City Univ Hong Kong Dept Math Hong Kong Peoples R China

This article is concerned with the distributed convex constrained optimization over a time-varying multiagent network in the non-Euclidean sense, where the bandwidth limitation of the network is considered. To save the network resources so as to reduce the communication costs, we apply an event-triggered strategy (ETS) in the information interaction of all the agents over the network. Then, an event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm, which utilizes the Bregman divergence as the distance-measuring function, is presented to investigate the multiagent optimization problem subject to a convex constraint set. Moreover, we also analyze the convergence of the developed ET-DSMD algorithm. An upper bound for the convergence result of each agent is established, which is dependent on the trigger threshold. It shows that a sublinear upper bound can be guaranteed if the trigger threshold converges to zero as time goes to infinity. Finally, a distributed logistic regression example is provided to prove the feasibility of the developed ET-DSMD algorithm.

关键词： optimization Convergence Mirrors convex functions Upper bound Machine learning algorithms Bandwidth Bregman divergence distributed convex optimization event-triggered communication strategy stochastic mirror descent algorithm

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distributed Primal-Dual Proximal Algorithms for convex optimization Involving Three Composite Functions

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2024年第1期11卷 389-401页

作者： Ran, Liang Li, Huaqing Hu, Jinhui Lu, Qingguo Wang, Zheng Li, Zhe Chen, Guo Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China Cent South Univ Dept Automat Changsha 410083 Peoples R China Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

This article develops a novel distributed primal-dua l proximal algorithm (PDPA-Dist) and its corresponding randomized version (Rand-PDPA-Dist) for solving convex optimization problems. The local objective consists of a smooth function and two possibly nonsmooth ones, with one involving a linear mapping. At each iteration, PDPA-Dist allows each agent to perform local computations by communicating with its neighbors, while Rand-PDPA-Dist is executed with a randomly and independently activated subset of agents. The proposed algorithms recover new distributed extensions of known centralized algorithms and existing distributed schemes, depending on certain special setups. Both PDPA-Dist and Rand-PDPA-Dist achieve exact linear convergence rates provided that local objective functions satisfy piecewise linear-quadratic or certain quadratic growth conditions. Finally, the performance and effectiveness of the proposed algorithms are demonstrated by resolving a distributed model predictive control (DMPC) problem.

关键词： Composite functions distributed convex optimization linear convergence primal-dual proximal algorithms randomized algorithm

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Double-Like Accelerated distributed optimization Algorithm for convex optimization Problem 10

Double-Like Accelerated Distributed Optimization Algorithm f...

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10th International Conference on Information Science and Technology (ICIST)

作者： Zhang, Keke Xiong, Jiang Dai, Xiangguang Chongqing Three Gorges Univ Sch Three Gorges Artificial Intelligence Chongqing 404100 Peoples R China

ISBN: (纸本)9781728155586

The optimization problem of minimizing the sum of local convex cost functions on undirected network is studied. Each local convex cost function in the network is accessed only by each node. To be able to get the desired result in an accelerated way, we propose a new double-like accelerated distributed optimization algorithm, named as DA-DOA, to solve the optimization problem over undirected networks. Two momentum terms and gradient tracking are introduced in DA-DOA, and the non-coordinated step-size is adopted at the same time. In the case that the cost function satisfies the general assumptions (smoothness and strong convexity), we prove that DA-DOA can quickly and linearly find the optimal solution of the problem when the step size and momentum coefficient are small enough and positive. Moreover, an explicit linear convergence rate is definitely shown. Finally, Finally, a number of simulation examples verify the validity of DA-DOA and the correctness of the analysis process.

关键词： distributed convex optimization momentum term gradient tracking uncoordinated step-sizes accelerated convergence

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distributed quantized mirror descent for strongly convex optimization over time-varying directed graph

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Science China(Information Sciences) 2022年第10期65卷 196-210页

作者： Menghui XIONG Baoyong ZHANG Deming YUAN Shengyuan XU School of Automation Nanjing University of Science and Technology

This paper investigates a distributed strongly convex constrained optimization problem in the non-Euclidean sense, where the bit rate of the considered communication between nodes is assumed to be limited, and the communication topology is represented by a time-varying directed graph. By considering the limitation of communication capacity, the quantization technique is applied in the process of exchanging information over the network. Then a distributed quantized mirror descent(DQMD) algorithm, which uses the Bregman divergence and time-varying quantizers, is developed for the strongly convex optimization under a convex constraint set. The convergence of the developed algorithm is also analyzed. It is shown that the nodes' state errors are bounded by some terms related to the quantization resolutions, and the sublinear upper-bounds can be guaranteed by choosing appropriate quantization resolutions. Finally, a distributed ridge regression is provided as an example to verify the validity of the proposed method.

关键词： distributed convex optimization strongly convex optimization mirror descent quantized communication Bregman divergence

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distributed Time-Varying optimization-Based Protocols for Affine Formation Maneuver

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2025年

作者： Su, Piaoyi Shi, Zhexin Yu, Jianglong Dong, Xiwang Ren, Zhang Wang, Danwei Beihang Univ Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China Beihang Univ Inst Unmanned Syst Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 63979 Singapore

In this work, an affine formation maneuver control problem is studied for second-order multiagent system. The agents' task is to achieve affine formation maneuver through local interaction while minimizing the global time-varying cost functions. First, a distributed time-varying optimization problem with affine formation constraints is presented, where the solution trajectory is the affine transformation of the desired nominal configuration. Second, distributed time-varying optimization-based protocols are proposed. Using the proposed protocols, the agents' states asymptotically converge to the optimal solution, and thus the desired affine formation and the collective maneuvers issues can be solved. Third, the asymptotic convergence is proved using Lyapunov arguments. Finally, the effectiveness of the protocols is demonstrated by numerical simulation and experimental examples.

关键词： Stress Protocols Cost function Multi-agent systems Laplace equations convex functions Convergence Trajectory Target tracking Formation control Affine formation maneuver distributed convex optimization multimobile robots platform time-varying cost functions

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Collaborative distributed AC Optimal Power Flow: A Dual Decomposition Based Algorithm

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Journal of Modern Power Systems and Clean Energy 2021年第6期9卷 1414-1423页

作者： Zheyuan Cheng Mo-Yuen Chow IEEE Department of Electrical and Computer Engineering North Carolina State University

We propose a dual decomposition based algorithm that solves the AC optimal power flow(ACOPF) problem in the radial distribution systems and microgrids in a collaborative and distributed manner. The proposed algorithm adopts the second-order cone program(SOCP) relaxed branch flow ACOPF model. In the proposed algorithm, bus-level agents collaboratively solve the global ACOPF problem by iteratively sharing partial variables with its 1-hop neighbors as well as carrying out local scalar computations that are derived using augmented Lagrangian and primal-dual subgradient methods. We also propose two distributed computing platforms, i. e., high-performance computing(HPC) based platform and hardware-in-theloop(HIL) testbed, to validate and evaluate the proposed algorithm. The computation and communication performances of the proposed algorithm are quantified and analyzed on typical IEEE test systems. Experimental results indicate that the proposed algorithm can be executed on a fully distributed computing structure and yields accurate ACOPF solution. Besides, the proposed algorithm has a low communication overhead.

关键词： distributed convex optimization distributed en-ergy management system optimal power flow primal-dual de-composition

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distributed continuous-time algorithm for a general nonsmooth monotropic optimization problem

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2019年第10期29卷 3252-3266页

作者： Li, Xiuxian Xie, Lihua Hong, Yiguang Nanyang Technol Univ Sch Elect & Elect Engn 50 Nanyang Ave Singapore 639798 Singapore Chinese Acad Sci Inst Syst Sci Key Lab Syst & Control Beijing Peoples R China

This paper investigates a general monotropic optimization problem for continuous-time networks, where the global objective function is a sum of local objective functions that are only known to individual agent, and general constraints are taken into account, including local inequality constraints, global equality constraint, and local feasible constraints. In addition, all functions involved in the objective functions and inequality constraints are not necessarily differentiable. To solve the problem, a distributed continuous-time algorithm is designed using subgradient projections, and it is shown that the proposed algorithm is well defined in the sense that the existence of its solutions can be guaranteed. Furthermore, it is proved that the algorithm converges to an optimal solution for the general monotropic optimization problem. Finally, a simulation example is provided for validating the theoretical result.

关键词： continuous-time networks distributed convex optimization general monotropic optimization problems nonsmooth analysis

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A stochastic averaging gradient algorithm with multi-step communication for distributed optimization

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OPTIMAL CONTROL APPLICATIONS & METHODS 2023年第4期44卷 2208-2226页

作者： Zheng, Zuqing Yan, Yu Feng, Liping Du, Zhenyuan Li, Huaqing Wang, Zheng Hu, Jinhui Xinzhou Teachers Univ Dept Comp Sci Xinzhou Peoples R China Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW Australia Cent South Univ Dept Automat Changsha Peoples R China

This paper studies distributed convex optimization problems over an undirected network where all nodes cooperate to minimize a sum of local objective functions. Each local objective function is further assumed to be an average of several convex instantaneous functions. By incorporating the stochastic averaging gradient into the distributed first-order primal-dual method, a stochastic averaging gradient algorithm with multi-step communication is proposed to solve the optimization problem. For each node, one randomly selected gradient of an instantaneous function is evaluated per iteration, which effectively reduces the computation cost of the algorithm. Based on conditions of strong convexity and Lipschitz continuity of the local instantaneous functions, a linear convergence rate of the proposed algorithm is guaranteed. Numerical simulations on the logistic regression problem demonstrate the performance of the algorithm and correctness of the theoretical results.

关键词： distributed convex optimization linear convergence rate multi-step communication stochastic averaging gradient

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Gossip Algorithms for convex Consensus optimization Over Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2011年第12期56卷 2911-2918页

作者： Lu, Jie Tang, Choon Yik Regier, Paul R. Bow, Travis D. Univ Oklahoma Sch Elect & Comp Engn Norman OK 73019 USA Stanford Univ Dept Mech Engn Stanford CA 94305 USA

In many applications, nodes in a network desire not only a consensus, but an optimal one. To date, a family of subgradient algorithms have been proposed to solve this problem under general convexity assumptions. This technical note shows that, for the scalar case and by assuming a bit more, novel non-gradient-based algorithms with appealing features can be constructed. Specifically, we develop Pairwise Equalizing (PE) and Pairwise Bisectioning (PB), two gossip algorithms that solve unconstrained, separable, convex consensus optimization problems over undirected networks with time-varying topologies, where each local function is strictly convex, continuously differentiable, and has a minimizer. We show that PE and PB are easy to implement, bypass limitations of the subgradient algorithms, and produce switched, nonlinear, networked dynamical systems that admit a common Lyapunov function and asymptotically converge. Moreover, PE generalizes the well-known Pairwise Averaging and Randomized Gossip Algorithm, while PB relaxes a requirement of PE, allowing nodes to never share their local functions.

关键词： distributed consensus distributed convex optimization gossip algorithms networked dynamical systems

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