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Distributed Asymptotic Minimization of Sequences of Convex Functions by a Broadcast Adaptive Subgradient Method

Distributed Asymptotic Minimization of Sequences of Convex Functions by a Broadcast Adaptive Subgradient Method
Distributed Asymptotic Minimization of Sequences of Convex Functions by a Broadcast Adaptive Subgradient Method
We propose a non-hierarchical decentralized algorithm for the asymptotic minimization of possibly time-varying convex functions. In our method, each agent in a network has a private, local (possibly time-varying) cost function, and the objective is to minimize asymptotically the sum of these local functions in every agent (this problem appears in many different applications such as, among others, motion planning, acoustic source localization, and environmental modeling). The algorithm consists of two main steps. First, to improve the estimate of a minimizer, agents apply a particular version of the adaptive projected subgradient method to their local functions. Then the agents exchange and mix their estimates using a communication model based on recent results of consensus algorithms. We show formally the convergence of the resulting scheme, which reproduces as particular cases many existing methods such as gossip consensus algorithms and recent decentralized adaptive subgradient methods (which themselves include as particular cases many distributed adaptive filtering algorithms). To illustrate two possible applications, we consider the problems of acoustic source localization and environmental modeling via network gossiping with mobile agents.
739-753
Cavalcante, Renato L. G.
8a5b50cd-3eb1-40ca-b805-c402396b9d9d
Rogers, Alex
f9130bc6-da32-474e-9fab-6c6cb8077fdc
Jennings, Nick
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Yamada, Isao
8e4dced2-ec02-4720-afdc-8768d3f6efe3
Cavalcante, Renato L. G.
8a5b50cd-3eb1-40ca-b805-c402396b9d9d
Rogers, Alex
f9130bc6-da32-474e-9fab-6c6cb8077fdc
Jennings, Nick
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Yamada, Isao
8e4dced2-ec02-4720-afdc-8768d3f6efe3

Cavalcante, Renato L. G., Rogers, Alex, Jennings, Nick and Yamada, Isao (2011) Distributed Asymptotic Minimization of Sequences of Convex Functions by a Broadcast Adaptive Subgradient Method. IEEE Journal of Selected Topics in Signal Processing, 5 (4), 739-753.

Record type: Article

Abstract

We propose a non-hierarchical decentralized algorithm for the asymptotic minimization of possibly time-varying convex functions. In our method, each agent in a network has a private, local (possibly time-varying) cost function, and the objective is to minimize asymptotically the sum of these local functions in every agent (this problem appears in many different applications such as, among others, motion planning, acoustic source localization, and environmental modeling). The algorithm consists of two main steps. First, to improve the estimate of a minimizer, agents apply a particular version of the adaptive projected subgradient method to their local functions. Then the agents exchange and mix their estimates using a communication model based on recent results of consensus algorithms. We show formally the convergence of the resulting scheme, which reproduces as particular cases many existing methods such as gossip consensus algorithms and recent decentralized adaptive subgradient methods (which themselves include as particular cases many distributed adaptive filtering algorithms). To illustrate two possible applications, we consider the problems of acoustic source localization and environmental modeling via network gossiping with mobile agents.

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Published date: 4 February 2011
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 271986
URI: https://eprints.soton.ac.uk/id/eprint/271986
PURE UUID: 9d14d781-07e8-4604-9b88-3b59857392d3

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Date deposited: 08 Feb 2011 09:04
Last modified: 19 Jul 2019 22:11

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Contributors

Author: Renato L. G. Cavalcante
Author: Alex Rogers
Author: Nick Jennings
Author: Isao Yamada

University divisions

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