Distributed primal–dual stochastic subgradient algorithms for multi‐agent optimization under inequality constraints

Yuan, Deming; Xu, Shengyuan; Zhang, Baoyong; Rong, Lina

doi:10.1002/rnc.2856

Cited by 28 publications

(22 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main idea is to estimate the optimal point by a consensus term plus a negative gradient term with deterministic or randomized iteration . To date, many researchers apply the consensus‐based distributed optimization algorithm to solve the problem and present a lot of results . However, the basis consensus‐based subgradient algorithms need to select the diminishing step sizes, which lead to the slow convergence rate.…”

Section: Introductionmentioning

confidence: 99%

“…3,7 To date, many researchers apply the consensus-based distributed optimization algorithm to solve the problem (1) and present a lot of results. [8][9][10][11] However, the basis consensus-based subgradient algorithms need to select the diminishing step sizes, which lead to the slow convergence rate. To overcome the drawbacks caused by the diminishing step sizes, some novel distributed optimization algorithms based on auxiliary-variables method are developed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed zero‐gradient‐sum algorithm for convex optimization with time‐varying communication delays and switching networks

Guo

Chen

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary The distributed convex optimization problem subject to time‐varying communication delays and switching network topologies is addressed in this paper. Based on continuous‐time Zero‐Gradient‐Sum scheme, the novel distributed algorithms are proposed to minimize the global objective function which is composed of a sum of strictly convex local cost functions. In the fixed network topology case, by constructing a new Lyapunov‐Krasovskii function, two explicit sufficient conditions for the maximum admissible time delay are derived to guarantee that all agents' states converge to the optimal solution. In the switching network topology case, the stability condition is derived by the common Lyapunov function theory. In addition, two sufficient conditions about the maximum admissible time delays are also derived for the fixed and switching weight‐balanced network topologies, respectively. Several simulation tests are used to illustrate the effectiveness of our obtained theoretical results.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed zero‐gradient‐sum algorithm for convex optimization with time‐varying communication delays and switching networks

Guo

Chen

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Recently, the problem of minimizing a sum of convex objective functions distributed among multiple agents over a network has attracted considerable attention, where each local objective function is known only to one agent in the network, and therefore, cooperation between agents is needed to reach a global objective . In contrast to the centralized optimization algorithm, a distributed algorithm has to take into account the communication and coordination in the process of optimization.…”

Section: Introductionmentioning

confidence: 99%

“…This paper focuses on another cooperation approach based on average consensus . In this case, each agent maintains its own estimate.…”

Section: Introductionmentioning

confidence: 99%

“…Because any utility function may be imperfectly observed by the agent itself due to the presence of random observation noise, extendedly, Reference considers the case of the noisy subgradients corrupted by stochastic errors and gives an exquisite stochastic analysis of the distributed projected consensus algorithm. In , the distributed primal‐dual stochastic subgradient algorithms are proposed for the synchronous time model case and the asynchronous case, respectively. Reference introduces a new framework for convergence analysis of distributed constrained non‐convex optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strong consistency of random gradient‐free algorithms for distributed optimization

Chen

Gao

2016

Optim Control Appl Methods

View full text Add to dashboard Cite

Summary A distributed multi‐agent convex optimization problem over a network with time‐varying connectivity is considered, where the agents are to collectively minimize a sum of nonsmooth but Lipschitz continuous functions subject to a convex constraint set. Based on Gaussian smoothing of the objective functions, a distributed projective random gradient‐free algorithm is considered for the constrained optimization problem, where each agent performs a local averaging operation, takes the one‐sided or two‐sided randomized gradient approximates instead of the subgradients to minimize its own objective function, and projects on the constraint set. The bounds on the limiting performance of the algorithm in mean are obtained, and it is proven that there is mean consensus between agents for diminishing step sizes. It is showed that with appropriately selected step sizes, the agent estimates generated by the algorithm converge to the same stationary point of the smoothed version of the problem with probability 1. Therefore, with sufficient small smoothing parameters, we obtain the result of consensus and convergence of the agent estimates to an optimal solution with probability 1. A numerical example is provided to justify the theoretical analysis. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

NNs‐Based Event‐Triggered Consensus Control of a Class of Uncertain Nonlinear Multi‐Agent Systems

Yang

Yue

2018

Asian Journal of Control

View full text Add to dashboard Cite

We are concerned with the consensus problem for a class of uncertain nonlinear multi-agent systems (MASs) connected through an undirected communication topology via event-triggered approaches in this paper. Two distributed control strategies, the adaptive centralized event-triggered control one and adaptive distributed event-triggered control one, are presented utilizing neural networks (NNs) and event-driven mechanisms, where the advantages of the proposed control laws lie that they remove the requirement for exact priori knowledge about parameters of individual agents by taking advantage of NNs approximators and they save computing and communication resources since control tasks only execute at certain instants with respect to predefined threshold functions. Also, the trigger coefficient can be regulated adaptively with dependence on state errors to ensure not only the control performance but also the efficiency of the network interactions. It is proven that all signals in the closed-loop system are bounded and the Zeno behavior is excluded. Finally, simulation examples are presented for illustration of the theoretical claims.

show abstract

Distributed primal–dual stochastic subgradient algorithms for multi‐agent optimization under inequality constraints

Cited by 28 publications

References 25 publications

Distributed zero‐gradient‐sum algorithm for convex optimization with time‐varying communication delays and switching networks

Distributed zero‐gradient‐sum algorithm for convex optimization with time‐varying communication delays and switching networks

Strong consistency of random gradient‐free algorithms for distributed optimization

NNs‐Based Event‐Triggered Consensus Control of a Class of Uncertain Nonlinear Multi‐Agent Systems

Contact Info

Product

Resources

About