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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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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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continuous-time algorithm for Distributed Nonsmooth Optimization via Decomposition Design 13

Continuous-Time Algorithm for Distributed Nonsmooth Optimiza...

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13th IEEE International Conference on Control & Automation (ICCA)

作者： Zhou, Hongbing Zeng, Xianlin Hong, Yiguang Chinese Acad Sci Inst Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China

ISBN: (纸本)9781538626795

This paper is concerned with a class of distributed nonsmooth convex constrained optimization problems with set constraints. The objective function is a sum of local convex functions, which are not necessarily differentiable. A new distributed continuous-time gradient-based algorithm using the decomposition design is explicitly constructed to solve the distributed optimization problem. Rigorous proofs using nonsmooth convex optimization theory and stability theory of differential inclusions are presented. A numerical simulation is conducted to show the efficacy of the proposed algorithm.

关键词： Distributed constrained optimization nonsmooth objective function continuous-time algorithm decomposition design

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continuous-time algorithm for distributed resource allocation over a weight-unbalanced digraph 31

Continuous-time algorithm for distributed resource allocatio...

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31st Chinese Control And Decision Conference (CCDC)

作者： Zhu, Yanan Yu, Wenwu Wen, Guanghui Chen, Duxin Southeast Univ Sch Math Jiangsu Prov Key Lab Networked Collect Intelligen Nanjing 210096 Peoples R China

ISBN: (纸本)9781728101057

This paper studies a resource allocation problem subject to the coupling resource constraint over a strongly connected and weight-unbalanced digraph, where the global cost function is composed of a sum of the agents's local cost functions. To solve the problem in a distributed way, we design a continuous-time algorithm by injecting a graph balancing technique into a primal-dual gradient How algorithm. We show that the optimal variable generated by the proposed algorithm asymptotically converges to the optimal solution when the local cost functions are strongly convex and and their gradients satisfy Lipschitz conditions. A numerical simulation verifies the theoretical result.

关键词： Distributed resource allocation continuous-time algorithm weight-unbalanced digraph

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An Adaptive continuous-time algorithm for Nonsmooth Convex Resource Allocation Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第11期67卷 6038-6044页

作者： Jia, Wenwen Liu, Na Qin, Sitian Harbin Inst Technol Dept Math Weihai 264209 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

This article develops a novel continuous-time algorithm based on the idea of adaptive strategy for solving a resource allocation optimization with nonsmooth objective functions and constraints over multiagent network. It is proved that the state solution is globally bounded and finally converges to an optimal solution to the nonsmooth convex resource allocation problem. Compared with the existing algorithms, the strong/strict convexity of the objective function is relaxed and only convexity is required. Moreover, by employing an exact penalty approach for the distributed optimization, the primal-dual variables is avoided to introduce. Therefore, the proposed algorithm has a simple structure with low dimensionality of state variables. To show the effectiveness and practicability of the presented algorithm, a numerical example and an application in power system are presented.

关键词： Optimization Resource management Complexity theory Aerospace electronics Technological innovation Linear programming Laplace equations continuous-time algorithm multiagent network resource allocation optimization

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A continuous-time algorithm for Distributed Optimization Based on Multiagent Networks

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2019年第12期49卷 2700-2709页

作者： He, Xing Huang, Tingwen Yu, Junzhi Li, Chaojie Zhang, Yushu Southwest Univ Natl & Local Joint Engn Lab Intelligent Transmiss Coll Elect & Informat Engn Chongqing 400715 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China Texas A&M Univ Qatar Dept Math Doha 23874 Qatar RMIT Univ Sch Elect & Comp Engn Melbourne Vic 3001 Australia Deakin Univ Sch Informat Technol Geelong Vic 3125 Australia

Based on the multiagent networks, this paper introduces a continuous-time algorithm to deal with distributed convex optimization. Using nonsmooth analysis and algebraic graph theory, the distributed network algorithm is modeled by the aid of a nonautonomous differential inclusion, and each agent exchanges information from the first-order and the second-order neighbors. For any initial point, the solution of the proposed network can reach consensus to the set of minimizers if the graph has a spanning tree. In contrast to the existing continuoustime algorithms for distributed optimization, the proposed model holds the least number of state variables and relaxes the strongly connected weighted-balanced topology to the weaker case. The modified form of the proposed continuous-time algorithm is also given, and it is proven that this algorithm is suitable for solving distributed problems if the undirected network is connected. Finally, two numerical examples and an optimal placement problem confirm the effectiveness of the proposed continuous-time algorithm.

关键词： continuous-time algorithm distributed optimization multiagent network

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Accelerated First-Order continuous-time algorithm for Solving Convex-Concave Bilinear Saddle Point Problem 21st

Accelerated First-Order Continuous-Time Algorithm for Solvin...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Zeng, Xianlin Dou, Lihua Chen, Jie Beijing Inst Technol Beijing Adv Innovat Ctr Intelligent Robots & Syst Key Lab Biomimet Robots Arid Syst Minist Educ Beijing Peoples R China Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Dept Control Sci & Engn Shanghai Peoples R China

First-order methods have simple structures and are of great importance to big data problems because first-order methods are easy to implement in a distributed or parallel way. However, in the worst cases, first-order methods often converge at a rate O(1/t), which is slow. This paper considers a class of convex-concave bilinear saddle point problems and proposes an accelerated first-order continuous-time algorithm. We design the accelerated algorithm by using both increasing and decreasing damping coefficients in the saddle point dynamics. If parameters of the proposed algorithm are proper, the algorithm owns O(1/t(2)) convergence without any strict or strong convexity requirement. Finally, we apply the algorithm to numerical examples to show the superior performance of the proposed algorithm over existing ones. Copyright (C) 2020 The Authors.

关键词： Accelerated method first-order algorithm continuous-time algorithm saddle-point problem

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Accelerated First-Order continuous-time algorithm for Solving Convex-Concave Bilinear Saddle Point Problem

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IFAC-PapersOnLine 2020年第2期53卷 7362-7367页

作者： Xianlin Zeng Lihua Dou Jie Chen Key Laboratory of Biomimetic Robots and Systems Beijing Advanced Innovation Center for Intelligent Robots and Systems Beijing Institute of Technology Ministry of Education Beijing China Department of Control Science and Engineering Tongji University the Shanghai Research Institute for Intelligent Autonomous Systems Shanghai China

First-order methods have simple structures and are of great importance to big data problems because first-order methods are easy to implement in a distributed or parallel way. However, in the worst cases, first-order methods often converge at a rate O(1/t), which is slow. This paper considers a class of convex-concave bilinear saddle point problems and proposes an accelerated first-order continuous-time algorithm. We design the accelerated algorithm by using both increasing and decreasing damping coefficients in the saddle point dynamics. If parameters of the proposed algorithm are proper, the algorithm owns O(1/ t 2 ) convergence without any strict or strong convexity requirement. Finally, we apply the algorithm to numerical examples to show the superior performance of the proposed algorithm over existing ones.

关键词： Accelerated method first-order algorithm continuous-time algorithm saddle-point problem

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A continuous-time primal-dual algorithm with convergence speed guarantee utilizing constraint-based control

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SICE JOURNAL OF CONTROL MEASUREMENT AND SYSTEM INTEGRATION 2025年第1期18卷

作者： Tanaka, Taichi Nakayama, Shunta Wasa, Yasuaki Hirata, Kenji Hatanaka, Takeshi Inst Sci Tokyo Sch Engn Dept Syst & Control Engn Tokyo Japan Waseda Univ Sch Adv Sci & Engn Dept Electr Engn & Biosci Tokyo Japan Univ Toyama Sch Engn Dept Elect & Elect Engn Toyama Japan

This paper proposes a novel continuous-time algorithm for solving optimization problems by leveraging the concept of so-called constraint-based control to guarantee a specific convergence speed. Conventional distributed optimization algorithms evaluate the convergence speed by the order of the convergence, which does not allow direct specification of the convergence speed. Moreover, the continuous-time version of the distributed optimization does not provide any convergence speed guarantee, with a few exceptions under a strong assumption. To address the issue, we incorporate constraint-based control into a typical continuous-time distributed optimization algorithm, namely primal-dual dynamics. Specifically, we introduce a constraint that ensures the desired increase rate of the dual function in the optimization problem. Our proposed method determines the update rules for the dual variables of the optimization problem by leveraging the present constraint. The proposed method is also shown to preserve the inherent distributed nature of the primal-dual dynamics. A numerical example demonstrates the effectiveness of our approach, highlighting not only the operability of the convergence speed but also the improvement of the convergence performance compared to the original primal-dual dynamics.

关键词： Primal-dual dynamics constraint-based control distributed optimization convergence rate continuous-time algorithm

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Distributed continuous-time Optimization of Second-Order Multiagent Systems With Nonconvex Input Constraints

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第10期51卷 6404-6413页

作者： Mo, Lipo Yu, Yongguang Zhao, Lin Cao, Xianbing Beijing Technol & Business Univ Sch Math & Stat Beijing 100048 Peoples R China Beijing Jiaotong Univ Dept Math Beijing 100044 Peoples R China Qingdao Univ Sch Automat Qingdao 266071 Peoples R China

This article discusses the distributed continuous-time optimization problem (DCTOP) of second-order multiagent systems (SOMASs). It is assumed that the inputs are required to be in some nonconvex sets, the team objective function (TOF) is a combination of general differentiable convex functions, and each agent can only obtain the information of one local objective function. Based on the neighbors' information, a new distributed continuous-time optimization algorithm (DCTOA) is first proposed for each agent, where its gradient gains are nonuniform. By introducing a scaling factor and a model transformation, the corresponding system is changed into a time-varying nonlinear system which does not contain constraint operator in form. Then, it is proven that all agents' states could reach an agreement and the TOF could be minimized by constructing some new Lyapunov functions. Finally, the effectiveness of the algorithm is shown by simulation results.

关键词： Optimization Multi-agent systems Linear programming Distributed algorithms Force Convergence Lyapunov methods Agreement continuous-time algorithm distributed optimization nonconvex constraints nonuniform gains second-order systems

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