Decentralized Resource Allocation in Dynamic Networks of Agents

Lakshmanan, Hariharan; Farias, Daniela Pucci de

doi:10.1137/060662228

Cited by 141 publications

(112 citation statements)

References 4 publications

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“…This growth rate is worse than the growth rate ln(n + 1) obtained in [18] for the global smoothing approximation, which uses a normally distributed perturbation vector z. However, it should be emphasized that the smoothing technique in [18] requires the function f to be defined over the entire space since z is drawn from a normal distribution, a somewhat stringent requirement.…”

Section: Local Randomized Smoothing Techniquementioning

confidence: 92%

“…Proof: (a) For the convexity and differentiability of f see the proof 4 of Lemma 3.3(a) in [18]. The gradient boundedness follows by Assumption 3, relation (6), and…”

Section: Local Randomized Smoothing Techniquementioning

confidence: 99%

“…However, it should be emphasized that the smoothing technique in [18] requires the function f to be defined over the entire space since z is drawn from a normal distribution, a somewhat stringent requirement. Our proposed local smoothing technique removes such a requirement, but suffers from a worse growth rate.…”

Section: Local Randomized Smoothing Techniquementioning

confidence: 99%

“…Furthermore, the gradient of the resulting differentiable function is Lipschitz continuous. This smoothing technique is motivated by the global smoothing technique proposed in [18]. In the remainder of the paper, we apply the local smoothing approach to both deterministic and stochastic convex optimization problems.…”

Section: Introductionmentioning

confidence: 99%

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Convex nondifferentiable stochastic optimization: A local randomized smoothing technique

Yousefian

Nedić

Shanbhag

2010

Proceedings of the 2010 American Control Conference

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Abstract-We consider a class of stochastic nondifferentiable optimization problems where the objective function is an expectation of a random convex function, that is not necessarily differentiable. We propose a local smoothing technique, based on random local perturbations of the objective function, that leads to a differentiable approximation of the function. Under the assumption that the local randomness originates from a uniform distribution, we establish a Lipschitzian property for the gradient of the approximation. This facilitates the development of a stochastic approximation framework, which now requires sampling in the product space of the original measure and the artificially introduced distribution. We show that under suitable assumptions, the resulting stochastic subgradient algorithm, with two samples per iteration, converges to an optimal solution of the problem for a diminishing stepsize when the subgradients are bounded.

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Section: Local Randomized Smoothing Techniquementioning

confidence: 92%

“…Proof: (a) For the convexity and differentiability of f see the proof 4 of Lemma 3.3(a) in [18]. The gradient boundedness follows by Assumption 3, relation (6), and…”

Section: Local Randomized Smoothing Techniquementioning

confidence: 99%

Section: Local Randomized Smoothing Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convex nondifferentiable stochastic optimization: A local randomized smoothing technique

Yousefian

Nedić

Shanbhag

2010

Proceedings of the 2010 American Control Conference

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“…Here we provide some examples. Lakshmanan and de Farias (2008) proposed a decentralized, asynchronous gradient-descent method that is suitable for implementation in the case where the communication between agents is described in terms of a dynamic network. Dominguez-Garcia et al…”

Section: Distributed Resource Allocationmentioning

confidence: 99%

Distributed coordination in multi-agent systems: a graph Laplacian perspective

Han

Lin

et al. 2015

Frontiers Inf Technol Electronic Eng

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This paper reviews some main results and progress in distributed multi-agent coordination from a graph Laplacian perspective. Distributed multi-agent coordination has been a very active subject studied extensively by the systems and control community in last decades, including distributed consensus, formation control, sensor localization, distributed optimization, etc. The aim of this paper is to provide both a comprehensive survey of existing literature in distributed multi-agent coordination and a new perspective in terms of graph Laplacian to categorize the fundamental mechanisms for distributed coordination. For different types of graph Laplacians, we summarize their inherent coordination features and specific research issues. This paper also highlights several promising research directions along with some open problems that are deemed important for future study.

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Distributed consensus time‐varying optimization algorithm for multi‐agent systems in predefined time via event‐triggered sliding mode control

Zhao,

Wu,

Cao

2024

Math Methods in App Sciences

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This paper proposes a distributed consensus algorithm in predefined time of time‐varying optimization with inequality constrains for multi‐agent systems (MASs) with external disturbances over an undirected graph. Firstly, by utilizing exponential function, a novel criterion with respect to the stability in predefined time is developed for the nonlinear systems. Secondly, a new distributed switching control protocol, which can inhibit the external unbounded disturbances, is piecewise designed to drive the states of agents to the sliding mode surface via the predefined‐time set by users. Subsequently, under the designed event‐triggered controller (ETC), the states of agents achieve consensus in predefined time on the sliding mode surface. Meanwhile, with the help of log barrier function, the consensus states of agents reach the feasible region and converge to the optimal solution in predefined time. Finally, the correctness and availability of the proposed optimization control algorithm are verified by a simulation example.

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Decentralized Resource Allocation in Dynamic Networks of Agents

Cited by 141 publications

References 4 publications

Convex nondifferentiable stochastic optimization: A local randomized smoothing technique

Convex nondifferentiable stochastic optimization: A local randomized smoothing technique

Distributed coordination in multi-agent systems: a graph Laplacian perspective

Distributed consensus time‐varying optimization algorithm for multi‐agent systems in predefined time via event‐triggered sliding mode control

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