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distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

AUTOMATICA 2015年 55卷 254-264页

作者： Kia, Solmaz S. Cortes, Jorge Martinez, Sonia Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92717 USA Univ Calif San Diego Dept Mech & Aerosp Engn San Diego CA 92103 USA

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Cooperative control distributed convex optimization Weight-balanced digraphs Event-triggered communication

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An Adaptive Dynamic Protocol for distributed convex optimization 34

An Adaptive Dynamic Protocol for Distributed Convex Optimiza...

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34th Chinese Control Conference (CCC)

作者： Huang, Aozhe Chen, Fei Lan, Weiyao Xiamen Univ Dept Automat Xiamen 361005 Fujian Peoples R China

ISBN: (纸本)9789881563897

This article considers the distributed convex optimization problem over a linear multi-agent system using an adaptive dynamic protocol. The communication network topology among the agents are assumed to be undirected and fixed. The global cost function of the network is strictly convex and is given by the sum of the local cost functions associated to each agents. It is proved that under the proposed protocol, the agents can reach an agreement on a common state value which optimizes the global cost function.

关键词： Multi-agent system distributed convex optimization undirected graph adaptive control

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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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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 Discrete-Time Algorithms for convex optimization With General Local Constraints on Weight-Unbalanced Digraph

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2021年第1期8卷 51-64页

作者： Liu, Hongzhe Zheng, Wei Xing Yu, Wenwu Southeast Univ Sch Math Nanjing 210096 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China Western Sydney Univ Sch Comp Data & Math Sci Sydney NSW 2751 Australia

This article investigates the convex optimization problem with general local constraints including N equality constraints, N inequality constraints, and N closed convex set constraints. Especially, the objective function of the considered problem is the sum of N convex functions, which are seen as local objective functions. First, for the distributed setting, a weight-unbalanced digraph with N nodes is introduced to describe the communication topology. Clearly, in the distributed setting, each node is responsible for a local objective function accompanied with an equality constraint, an inequality constraint, and a closed convex set constraint, which are viewed as local constraints. The aim of this article is to solve the considered convex optimization problem in a distributed manner, i.e., to lead the states of all nodes to a common optimal solution of the considered problem under the condition that each node only knows its own local objective function, and local constraints, and the information of its neighbors' states. Towards this end, by resorting to the exact penalty function method and the gradient descent-like method, two distinct distributed discrete-time algorithms are developed for two different cases, respectively. Furthermore, the convergence properties of the designed algorithms are rigorously analyzed under some common and standard assumptions, and the convergence rates are described in detail. Finally, simulation results are provided to verify the theoretical results.

关键词： Directed topology discrete-time algorithm distributed convex optimization general local constraints

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distributed continuous-time constrained convex optimization with general time-varying cost functions

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2021年第6期31卷 2222-2236页

作者： Huang, Bomin Zou, Yao Meng, Ziyang Tsinghua Univ Dept Precis Instrument Beijing 100084 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China

The distributed time-varying constrained convex optimization problem over a connected undirected network topology is studied in this article. The proposed distributed optimization algorithm is composed of a projection map term, a consensus term, and a gradient term, and is feasible for any initial condition. We first show that the states of the optimization algorithm uniformly converge to a neighborhood of the constraint set while an approximate global consensus is achieved. Then the states are proven to uniformly converge to a neighborhood of the time-varying optimal trajectory. The theoretical results are validated by some simulations.

关键词： constraint set distributed convex optimization time‐ varying cost function

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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 Continuous-Time Nonsmooth convex optimization With Coupled Inequality Constraints

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2020年第1期7卷 74-84页

作者： Li, Xiuxian Xie, Lihua Hong, Yiguang Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Chinese Acad Sci Inst Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China

This paper studies distributed convex optimization problems over continuous-time multiagent networks subject to two types of constraints, i.e., local feasible set constraints and coupled inequality constraints, where all involved functions are not necessarily differentiable, only assumed to be convex. In order to solve this problem, a modified primal-dual continuous-time algorithm is proposed by projections on local feasible sets. With the aid of constructing a proper Lyapunov function candidate, the existence of solutions of the algorithm in the Caratheodory sense and the convergence of the algorithm to an optimal solution for the distributed optimization problem are established. Additionally, a sufficient condition is provided for making the algorithm fully distributed. Finally, the theoretical result is corroborated by a simulation example.

关键词： Continuous-time algorithms coupled inequality constraints distributed convex optimization multiagent networks nonsmooth analysis

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Projected Primal-Dual Dynamics for distributed Constrained Nonsmooth convex optimization

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IEEE TRANSACTIONS ON CYBERNETICS 2020年第4期50卷 1776-1782页

作者： Zhu, Yanan Yu, Wenwu Wen, Guanghui Chen, Guanrong Southeast Univ Sch Math Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3000 Australia City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China

A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle's invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal-dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.

关键词： optimization convex functions Heuristic algorithms Linear programming Convergence Cybernetics Indexes distributed convex optimization multiagent networks nonsmooth analysis primal-dual dynamics

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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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