Distributed proximal‐gradient algorithms for nonsmooth convex optimization of second‐order multiagent systems

Wang, Qing; Chen, Jie; Zeng, Xianlin; Xin, Bin

doi:10.1002/rnc.5199

Cited by 22 publications

(7 citation statements)

References 40 publications

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“…The authors of [32] presented a distributed quasimonotone subgradient algorithm for non-smooth convex optimisation over directed graphs. For the distributed non-smooth convex optimisation problems in second-order multiagent systems, the authors of [33] recently developed a novel continuoustime distributed proximal-gradient algorithms with derivative feedback. Motivated by these excellent efforts [31][32][33], it would be of interest to focus on investigating distributed online learning algorithms to obtain dynamic regret bounds for non-smooth or non-convex objective functions over time-varying networks in the future work.…”

Section: Discussionmentioning

confidence: 99%

A conditional gradient algorithm for distributed online optimization in networks

Shen

Fang

et al. 2020

IET Control Theory & Appl

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This paper addresses a network of computing nodes aiming to solve an online convex optimisation problem in a distributed manner, that is, by means of the local estimation and communication, without any central coordinator. An online distributed conditional gradient algorithm based on the conditional gradient is developed, which can effectively tackle the problem of high time complexity of the distributed online optimisation. The proposed algorithm allows the global objective function to be decomposed into the sum of the local objective functions, and nodes collectively minimise the sum of local time-varying objective functions while the communication pattern among nodes is captured as a connected undirected graph. By adding a regularisation term to the local objective function of each node, the proposed algorithm constructs a new time-varying objective function. The proposed algorithm also utilises the local linear optimisation oracle to replace the projection operation such that the regret bound of the algorithm can be effectively improved. By introducing the nominal regret and the global regret, the convergence properties of the proposed algorithm are also theoretically analysed. It is shown that, if the objective function of each agent is strongly convex and smooth, these two types of regrets grow sublinearly with the order of O(log T ), where T is the time horizon. Numerical experiments also demonstrate the advantages of the proposed algorithm over existing distributed optimisation algorithms.

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Section: Discussionmentioning

confidence: 99%

A conditional gradient algorithm for distributed online optimization in networks

Shen

Fang

et al. 2020

IET Control Theory & Appl

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“…In Reference 12. a distributed optimization system analysis and design method from the viewpoint of control system is proposed. Then, various of continuous-time systems began to be studied, and a great of continuous-time distributed algorithms [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] have been considered to tackle distributed optimization problem for continuous-time systems in last past decade. In Reference 17, an edge-based adaptive algorithm is designed for multi-agent systems with general linear dynamics.…”

Section: Introductionmentioning

confidence: 99%

Distributed optimization for a class of uncertain nonlinear multi‐agent systems with arbitrary relative degree subject to exogenous disturbances

Liu

2022

Intl J Robust & Nonlinear

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This paper studies the distributed optimization problem on the framework of a class of arbitrary relative degree uncertain nonlinear multi‐agent systems with the presence of exogenous disturbances. Based on the internal model principle and the pseudo gradient approach, a novel continuous‐time distributed optimization control protocol is proposed to make all the agents reach optimal consensus by utilizing local cost functions information and neighbors' states information. The main advantage of our algorithm is that it can run on systems with more complex dynamics, while the existing algorithms apply only to integral‐type systems or unity relative degree nonlinear systems. Moreover, the convergence of the algorithm is proved by Lyapunov function and graph theory analysis. Finally, the distributed protocol is physically implemented by circuits and tested on a group of Chua's circuit systems to show the effectiveness of the theoretical results.

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“…Distributed optimization with multi‐agent networks has received considerable attention in diverse engineering problems, such as machine learning, 1 shortest distance optimization, 2 deception attacks, 3 mobile manipulators cooperative transportation, 4 smart grids, 5 resource allocation, 6,7 monotropic optimization problem 8 and so on. In the light of target decision variables being consistent or not, there are two types of distributed optimization problems in the literature.…”

Section: Introductionmentioning

confidence: 99%

Distributed optimization with hybrid linear constraints for multi‐agent networks

Zheng

Liu

Wang

2021

Intl J Robust & Nonlinear

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This article investigates the distributed constrained optimization with hybrid linear constraints for multi‐agent networks, in which all the agents collaboratively minimize the global objective function with a sum of convex local objective functions, while the constraints are more general with local and global restrictions on the agents. Based on matrix and graph theories, a discrete‐time algorithm under distributed manner is designed to deal with the organized problems. In addition, the optimality of the presented algorithm is obtained under certain initial restriction for the agents. By virtue of a novel Lyapunov function and the optimal conditions, rigorous analysis shows the convergence of the multi‐agent networks with undirected and connected graphs. Finally, two simulation examples are presented to validate the theoretical consequence.

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Distributed proximal‐gradient algorithms for nonsmooth convex optimization of second‐order multiagent systems

Cited by 22 publications

References 40 publications

A conditional gradient algorithm for distributed online optimization in networks

A conditional gradient algorithm for distributed online optimization in networks

Distributed optimization for a class of uncertain nonlinear multi‐agent systems with arbitrary relative degree subject to exogenous disturbances

Distributed optimization with hybrid linear constraints for multi‐agent networks

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