Distributed estimation via dual decomposition

Samar, S.; Boyd, Stephen; Gorinevsky, D.

doi:10.23919/ecc.2007.7069016

Cited by 47 publications

(31 citation statements)

References 15 publications

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“…Distributed implementation of optimization problems is an important field of research in distributed systems [15,4]. In many optimization problems the joint state space of all the search variables is too big or too complex for the optimization problem to be solved centrally.…”

Section: Introductionmentioning

confidence: 99%

Distributed Optimization with Pairwise Constraints and its Application to Multi-robot Path Planning

Bhattacharya

Kumar

Likhachev

2010

Robotics: Science and Systems VI

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Abstract-Distributed approaches to constrained optimization problems have immense applications to multi-robot path planning, scheduling, task allocation and other problems requiring multiple robots to optimize a global objective function. The aim of these approaches is to solve a series of smaller optimization problems for each robot while sharing information among the robots, and in the process, solve the global optimization problem, which otherwise would have been intractable. Distributed approaches to separable convex optimization problems with linear constraints have been studied extensively in the past using techniques of dual and Lagrangian decomposition. In the present work, we investigate a distributed implementation of a general separable optimization problem with pair-wise non-linear constraints. On the theoretical side, we show the conditions under which the algorithm converges to an optimal solution. On the experimental side, we demonstrate the utility of the algorithm on the problem of multi-robot path planning with pair-wise distance constraints in large complex 2-D environments with obstacles.

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Section: Introductionmentioning

confidence: 99%

Distributed Optimization with Pairwise Constraints and its Application to Multi-robot Path Planning

Bhattacharya

Kumar

Likhachev

2010

Robotics: Science and Systems VI

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“…It was utilized as an important sub-routine for designing parallel, distributed algorithms for a class of optimization problems [2]. More recently, inspired by applications in sensor and peerto-peer networks, robust and randomized variants of such algorithms have been studied [7], [12]. In these and other works such as [13], the algorithm's running time was tied with topological property of the communication network graph.…”

Section: B Related Workmentioning

confidence: 99%

Fast averaging

Bodas

Shah

2011

2011 IEEE International Symposium on Information Theory Proceedings

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Abstract-We are interested in the following question: given n numbers x1, . . . , xn, what sorts of approximation of average xave = 1 n (x1 + · · · + xn) can be achieved by knowing only r of these n numbers. Indeed the answer depends on the variation in these n numbers. As the main result, we show that if the vector of these n numbers satisfies certain regularity properties captured in the form of finiteness of their empirical moments (third or higher), then it is possible to compute approximation of xave that is within 1 ± ε multiplicative factor with probability at least 1 − δ by choosing, on an average, r = r(ε, δ, σ) of the n numbers at random with r is dependent only on ε, δ and the amount of variation σ in the vector and is independent of n.The task of computing average has a variety of applications such as distributed estimation and optimization, a model for reaching consensus and computing symmetric functions. We discuss implications of the result in the context of two applications: load-balancing in a computational facility running MapReduce, and fast distributed averaging.

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“…We call this form the Overlapping Cluster Decomposition. We then apply the framework for dual decomposition described by Samar et al for convex optimization problems with a separable objective and coupling constraints [13] to derive a distributed algorithm that solves the optimization problem.…”

Section: A Overlapping Cluster Dual Decompositionmentioning

confidence: 99%

Network optimization with dynamic demands and link prices

Patterson

Wittie

Almeroth

et al. 2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-We present Overlapping Cluster Decomposition (OCD), a novel distributed algorithm for network optimization targeted for networks with dynamic demands and link prices. OCD uses a dual decomposition of the global problem into local optimization problems in each node's neighborhood. The local solutions are then reconciled to find the global optimal solution. While OCD is a descent method and thus may converge slowly in a static network, we show that OCD can more rapidly adapt to changing network conditions than previously proposed firstorder and Newton-like network optimization algorithms. Therefore, OCD yields better solutions over time than previously proposed methods at a comparable communication cost.

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Distributed estimation via dual decomposition

Cited by 47 publications

References 15 publications

Distributed Optimization with Pairwise Constraints and its Application to Multi-robot Path Planning

Distributed Optimization with Pairwise Constraints and its Application to Multi-robot Path Planning

Fast averaging

Network optimization with dynamic demands and link prices

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