Solving a class of nonsmooth resource allocation problems with directed graphs through distributed Lipschitz continuous multi-proximal algorithms

Wei, Yue; Shang, Chengsi; Fang, Hao; Zeng, Xianlin; Dou, Lihua; Pardalos, Pãnos M.

doi:10.1016/j.automatica.2021.110071

Cited by 9 publications

(4 citation statements)

References 25 publications

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“…Remark Compared with the existing distributed resource allocation algorithms with explicit gradient information of cost functions, 9‐20 algorithm (6) is designed with the unknown cost functions. The estimation of gradient information, obtained by the extremum seeking control with the values of cost functions, replaces the explicit gradient information in the above‐mentioned algorithms.…”

Section: Resultsmentioning

confidence: 99%

“…The estimation of gradient information, obtained by the extremum seeking control with the values of cost functions, replaces the explicit gradient information in the above-mentioned algorithms. Moreover, the above-mentioned distributed algorithms [9][10][11][12][13][14][15][16][17][18][19][20] are invalid in the application of multi-agent systems with input dead-zone.…”

Section: Lemma 4 (Theorem 1 In the Work Ofmentioning

confidence: 99%

“…In recent years, the distributed resource allocation problem for multi‐agent systems has attracted an increasing interest as it involves a variety of applications, such as communication networks, 1‐3 sensor networks 4,5 and smart grids 6‐8 . Based on the primal‐dual dynamics, numerous distributed resource allocation algorithms have been proposed for agents who know their own cost functions with the explicit expression 9‐20 …”

Section: Introductionmentioning

confidence: 99%

“…[6][7][8] Based on the primal-dual dynamics, numerous distributed resource allocation algorithms have been proposed for agents who know their own cost functions with the explicit expression. [9][10][11][12][13][14][15][16][17][18][19][20] However, in some practical engineering systems, cost functions may be unknown due to the existence of uncertain or unknown parameters, such as unknown position information or environment conditions in sensor networks, 21,22 uncertain traffic demands in the network routing 23 and the unknown price functions in energy markets. 6,24 To deal with the resource allocation problem with unknown cost functions, some results have been reported.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Distributed extremum‐seeking based resource allocation algorithm with input dead‐zone

Cai

Zhong²,

Li³

et al. 2023

Intl J Robust & Nonlinear

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This paper studies distributed resource allocation problem for agents with input dead-zone, which is not considered in the existing work. At first, the primal problem is transformed to an auxiliary problem by using the exact penalty method to deal with local inequality constraints. It is assumed that the explicit expressions of cost functions and local inequality constraints are unknown to agents but the values of the cost and constraint functions can be obtained. Under such a setup, the extremum seeking control is used to estimate the gradient information. Thus, to obtain the optimal allocation, a novel distributed algorithm is designed by the virtue of the extremum seeking control and a dynamic compensating mechanism which is used to handle the effects of the input dead-zone. Due to a two time-scale structure of the designed distributed algorithm, the semi-globally practically asymptotical convergence of all agents' decisions to the optimal allocation is obtained by the singular perturbation technique. Finally, numerical examples of economic dispatch in smart grids are given to verify the effectiveness of our proposed method.

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Section: Resultsmentioning

confidence: 99%

Section: Lemma 4 (Theorem 1 In the Work Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Distributed extremum‐seeking based resource allocation algorithm with input dead‐zone

Cai

Zhong²,

Li³

et al. 2023

Intl J Robust & Nonlinear

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Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem

Wang

Qin

2022

J Syst Sci Complex

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A collective neurodynamic approach to distributed resource allocation with event-triggered communication

Cai,

Gao,

Nan

2024

Complex Intell. Syst.

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To solve a distributed optimal resource allocation problem, a collective neurodynamic approach based on recurrent neural networks (RNNs) is proposed in this paper. Multiple RNNs cooperatively solve a global constrained optimization problem in which the objective function is a total of local non-smooth convex functions and is subject to local convex sets and a global equality constraint. Different from the projection dynamics to deal with local convex sets in the existing work, an internal dynamics with projection output is designed in the algorithm to relax the Slater’s condition satisfied by the optimal solution. To overcome continuous-time communication in a group of RNNs, an aperiodic communication scheme, called the event-triggered scheme, is presented to alleviate communication burden. It is analyzed that the convergence of the designed collective neurodynamic approach based on the event-triggered communication does not rely on global information. Furthermore, it is proved the freeness of the Zeno behavior in the event-triggered scheme. Two examples are presented to illustrate the obtained results

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Solving a class of nonsmooth resource allocation problems with directed graphs through distributed Lipschitz continuous multi-proximal algorithms

Cited by 9 publications

References 25 publications

Distributed extremum‐seeking based resource allocation algorithm with input dead‐zone

Distributed extremum‐seeking based resource allocation algorithm with input dead‐zone

Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem

A collective neurodynamic approach to distributed resource allocation with event-triggered communication

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