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distributed nonconvex optimization subject to globally coupled constraints via collaborative neurodynamic optimization

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NEURAL NETWORKS 2025年 184卷 107027页

作者： Xia, Zicong Liu, Yang Hu, Cheng Jiang, Haijun Southeast Univ Sch Math Nanjing 210096 Peoples R China Zhejiang Normal Univ Sch Math Sci Jinhua 321004 Peoples R China Xinjiang Univ Coll Math & Syst Sci Urumqi 830017 Peoples R China Yili Normal Univ Sch Math & Stat Yining 835000 Peoples R China

In this paper, a recurrent neural network is proposed for distributed nonconvex optimization subject to globally coupled (in)equality constraints and local bound constraints. Two distributed optimization models, including a resource allocation problem and a consensus-constrained optimization problem, are established, where the objective functions are not necessarily convex, or the constraints do not guarantee a convex feasible set. To handle the nonconvexity, an augmented Lagrangian function is designed, based on which a recurrent neural network is developed for solving the optimization models in a distributed manner, and the convergence to a local optimal solution is proven. For the search of global optimal solutions, a collaborative neurodynamic optimization method is established by utilizing multiple proposed recurrent neural networks and a meta- heuristic rule. A numerical example, a simulation involving an electricity market, and a distributed cooperative control problem are provided to verify and demonstrate the characteristics of the main results.

关键词： distributed nonconvex optimization Augmented Lagrangian function Recurrent neural network Collaborative neurodynamic optimization

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A reformulation neurodynamic algorithm for distributed nonconvex optimization

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NEUROCOMPUTING 2025年 635卷

作者： Yu, Xin Huang, Qingzhou Lin, Rixin Guangxi Univ Dept Comp & Elect Informat Nanning 530004 Guangxi Peoples R China Guangxi Key Lab Multimedia Commun & Network Techno Nanning 530004 Guangxi Peoples R China

This paper presents a reformulation neurodynamic algorithm for solving distributed nonconvex optimization problems. A class of general Lagrangian functions is introduced to eliminate the dual gap in nonconvex problems. This algorithm extends the application of neurodynamic algorithms based on the p-power reformulation transformation of Lagrangian functions. Under mild conditions, the initial point of the decision vector can be arbitrarily chosen. It is proven that the output trajectories will eventually converge to a strict local minimum point of the distributed nonconvex optimization problem. Finally, numerical experiments demonstrate the effectiveness of the proposed algorithm, which is also applied to solve the oblique throwing problem and the distributed source localization problem.

关键词： distributed nonconvex optimization Partial reformulation Neurodynamic algorithm

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Momentum-Based Multiagent Approaches to distributed nonconvex optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第5期70卷 3331-3338页

作者： Xia, Zicong Liu, Yang Kou, Kit Ian Lu, Jianquan Gui, Weihua Zhejiang Normal Univ Sch Math Sci Jinhua 321004 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Zhejiang Normal Univ Key Lab Intelligent Educ Technol & Applicat Jinhua 321004 Peoples R China Zhejiang Normal Univ Hangzhou Sch Automat Hangzhou 311231 Peoples R China Univ Macau Fac Sci & Technol Dept Math Macau 999078 Peoples R China Cent South Univ Sch Automat Changsha 410083 Peoples R China

In this article, a paradigm of momentum-based systems is introduced for nonconvex optimization. Based on the paradigm, a momentum-based system and a momentum-based multiagent system are developed for nonconvex constrained optimization and distributed nonconvex optimization, respectively, and the convergence and convergence rate to a local optimal solution are proven. In addition, a hybrid swarm intelligence algorithm is established, which consists of multiple momentum-based systems for scattering searches and a meta-heuristic rule for repositioning the states upon their local convergence. Two numerical examples are elaborated to verify and demonstrate the optimality, enhanced stability, and faster convergence of the proposed approaches.

关键词： optimization Convergence Linear programming Particle swarm optimization Convex functions Security Scalability Recurrent neural networks Power system stability Neurodynamics distributed nonconvex optimization momentum-based optimization multiagent systems (MASs)

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distributed nonconvex optimization for Energy Efficiency in Mobile Ad Hoc Networks

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IEEE SYSTEMS JOURNAL 2021年第4期15卷 5683-5693页

作者： Hashempour, Saeed Suratgar, Amir Abolfazl Afshar, Ahmad Amirkabir Univ Technol Dept Elect Engn Tehran *** Iran Amirkabir Univ Technol Distributed & Intelligent Optimizat Res Lab DiorL Tehran *** Iran

This article proposes a distributed nonconvex optimization algorithm for energy efficiency (EE) in mobile ad hoc networks (MANETs). The proposed model for EE in MANETs can be classified into the category of nonconvex optimization problems. There are various distributed algorithms for solving nonconvex optimization problems. But, they are associated with some flaws such as complexity of implementation and low convergence rate. In this regard, in addition to the simplicity in implementation, the optimal point of the proposed model is a saddle point. Using augmented Lagrangian function with continuous-time optimization dynamics algorithm, a dynamic system will be established where its equilibrium points are Karush-Kuhn-Tucker points of the proposed model. Also, it will be shown that these points can be locally asymptotically stable under some conditions. Additionally, the proposed analytic method proves that the rate of convergence increases with an increasing penalty coefficient. To validate the performance of the presented algorithm, the problem of EE optimization for a sample mobile ad hoc network is simulated in MATLAB environment.

关键词： optimization Heuristic algorithms Mathematical model Mobile computing Mobile ad hoc networks Cost function Convergence Continuous-time optimization dynamics distributed nonconvex optimization energy efficiency mobile ad hoc networks (MANETs) wireless communications

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A Primal-Dual SGD Algorithm for distributed nonconvex optimization

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IEEE/CAA Journal of Automatica Sinica 2022年第5期9卷 812-833页

作者： Xinlei Yi Shengjun Zhang Tao Yang Tianyou Chai Karl Henrik Johansson Division of Decision and Control Systems School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technologyand also affiliated with the Digital FuturesStockholm 10044Sweden Department of Electrical Engineering University of North TexasDentonTX 76203 USA IEEE State Key Laboratory of Synthetical Automation for Process Industries Northeastern UniversityShenyang 110819China

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is *** problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated *** propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost *** show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of *** also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global *** demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.

关键词： distributed nonconvex optimization linear speedup Polyak-Lojasiewicz(P-L)condition primal-dual algorithm stochastic gradient descent

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Linear Convergence of First- and Zeroth-Order Primal-Dual Algorithms for distributed nonconvex optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第8期67卷 4194-4201页

作者： Yi, Xinlei Zhang, Shengjun Yang, Tao Chai, Tianyou Johansson, Karl H. KTH Royal Inst Technol Sch Elect Engn & Comp Sci Div Decis & Control Syst S-11428 Stockholm Sweden Digital Futures S-11428 Stockholm Sweden Univ North Texas Dept Elect Engn Denton TX 76203 USA Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China

This article considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual algorithm. We show that it converges sublinearly to a stationary point if each local cost function is smooth and linearly to a global optimum under an additional condition that the global cost function satisfies the Polyak-Lojasiewicz condition. This condition is weaker than strong convexity, which is a standard condition for proving linear convergence of distributed optimization algorithms, and the global minimizer is not necessarily unique. Motivated by the situations where the gradients are unavailable, we then propose a distributed zeroth-order algorithm, derived from the considered first-order algorithm by using a deterministic gradient estimator, and show that it has the same convergence properties as the considered first-order algorithm under the same conditions. The theoretical results are illustrated by numerical simulations.

关键词： Convergence Cost function Convex functions Costs Technological innovation Lyapunov methods Laplace equations distributed nonconvex optimization first-order algorithm linear convergence primal-dual algorithm zeroth-order algorithm

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A p-power neurodynamic approach to distributed nonconvex optimization

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2024年 134卷

作者： Li, Yangxia Xia, Zicong Liu, Yang Cao, Jinde Abdel-Aty, Mahmoud Zhejiang Normal Univ Sch Math Sci Jinhua 321004 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Zhejiang Normal Univ Key Lab Intelligent Educ Technol & Applicat Zhejia Jinhua 321004 Peoples R China Linyi Univ Sch Automat & Elect Engn Linyi 276005 Peoples R China Ahlia Univ Manama Bahrain Ahlia Univ Grad Studies & Sci Res Manama Bahrain Sohag Univ Fac Sci Math Dept Sohag 82524 Egypt

In this paper, a neurodynamic optimization approach based on a p -power transformation Lagrangian function is developed for distributed nonconvex optimization. A new Lagrangian function is proposed to eliminate dual gaps of nonconvex problems, and a distributed average tracking approach is developed for estimating global objective function value. Based on the Lagrangian function and the distributed average tracking approach, a neurodynamic model is developed for distributed nonconvex optimization, and its convergence to a local minimum is proven. Two numerical examples are provided to demonstrate the validity and effectiveness of the proposed approach.

关键词： distributed nonconvex optimization p-power transformation Neurodynamic optimization

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Guaranteed Privacy of distributed nonconvex optimization via Mixed-Monotone Functional Perturbations

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IEEE CONTROL SYSTEMS LETTERS 2023年 7卷 1081-1086页

作者： Khajenejad, Mohammad Martinez, Sonia Univ Calif San Diego Dept Mech & Aerosp Engn San Diego CA 92122 USA

In this letter, we introduce a new notion of guaranteed privacy for distributed nonconvex optimization algorithms. In particular, leveraging mixed-monotone inclusion functions, we propose a privacy-preserving mechanism which is based on deterministic, but unknown affine perturbations of the local objective functions. The design requires a robust optimization method to characterize the best accuracy that can be achieved by an optimal perturbation. This is used to guide the refinement of a guaranteed-private perturbation mechanism that can achieve a quantifiable accuracy via a theoretical upper bound that is independent of the chosen optimization algorithm. Finally, simulation results illustrate the accuracy-privacy trade-off and that our approach outperforms a benchmark differentially private distributed optimization algorithm in the literature.

关键词： Privacy Perturbation methods optimization Linear programming Differential privacy Jacobian matrices Upper bound distributed nonconvex optimization functional perturbations guaranteed privacy

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A Communication-Efficient Stochastic Gradient Descent Algorithm for distributed nonconvex optimization 18

A Communication-Efficient Stochastic Gradient Descent Algori...

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IEEE 18th International Conference on Control and Automation (ICCA)

作者： Xie, Antai Yi, Xinlei Wang, Xiaofan Cao, Ming Ren, Xiaoqiang Shanghai Univ Sch Mechatron Engn & Automat Shanghai Peoples R China MIT Lab Informat & Decis Syst Cambridge MA 02139 USA Univ Groningen Fac Sci & Engn Groningen Netherlands

ISBN: (纸本)9798350354416;9798350354409

This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We propose a distributed stochastic gradient descent algorithm, suitable for a general class of compressors. We show that the proposed algorithm achieves the linear speedup convergence rate O(1/root nT) for smooth nonconvex functions, where T and n are the number of iterations and agents, respectively. If the global cost function additionally satisfies the Polyak-Lojasiewicz condition, the proposed algorithm can linearly converge to a neighborhood of the global optimum, regardless of whether the stochastic gradient is unbiased or not. Numerical experiments are carried out to verify the efficiency of our algorithm.

关键词： distributed nonconvex optimization linear speedup compressed communication stochastic gradient

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Quantized Gradient Descent Algorithm for distributed nonconvex optimization

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2023年第10期E106A卷 1297-1304页

作者： Yoshida, Junya Hayashi, Naoki Takai, Shigemasa Osaka Univ Grad Sch Engn Suita 5650871 Japan Osaka Univ Grad Sch Engn Sci Toyonaka 5608531 Japan

This paper presents a quantized gradient descent algorithm for distributed nonconvex optimization in multiagent systems that takes into account the bandwidth limitation of communication channels. Each agent encodes its estimation variable using a zoom-in parameter and sends the quantized intermediate variable to the neighboring agents. Then, each agent updates the estimation by decoding the received information. In this paper, we show that all agents achieve consensus and their estimated variables converge to a critical point in the optimization problem. A numerical example of a nonconvex logistic regression shows that there is a trade-off between the convergence rate of the estimation and the communication bandwidth.

关键词： key multiagent system distributed nonconvex optimization cooperative control

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