Control approach to distributed optimization

Wang, Jing; Elia, Nicola

doi:10.1109/allerton.2010.5706956

Cited by 294 publications

(219 citation statements)

References 7 publications

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“…• Remark 5.7 (Discrete-time counterpart of (6) and (11)): It is worth noticing that the discretization of (6) for undirected graphs (performed in [12] for the case of continuously differentiable, strictly convex functions) and (11) for weight-balanced digraphs gives rise to different discretetime optimization algorithms from the ones considered in [1], [2], [3], [4], [5], [6].…”

Section: Lemma 53mentioning

confidence: 99%

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Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs

Gharesifard

Cortés

2014

IEEE Trans. Automat. Contr.

707

377

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This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge, on any strongly connected weightbalanced digraph, to the set of minimizers of a sum of convex differentiable functions with globally Lipschitz gradients. Our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results.

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Section: Lemma 53mentioning

confidence: 99%

“…Here, we review the continuous-time solution to the optimization problem proposed in [12], [13] for undirected graphs. If G is undirected, the gradient of F in (5) is distributed over G.…”

Section: Continuous-time Distributed Optimization On Undirected Nmentioning

confidence: 99%

Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs

Gharesifard

Cortés

2014

IEEE Trans. Automat. Contr.

707

377

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“…The algorithm for distributed convex optimization in continuous-time was firstly proposed in [23,24], but they were second order. The work [6] also proposed a continuous-time algorithm, but of the observer type.…”

Section: Results and Concluding Remarkmentioning

confidence: 99%

“…Along the line of continuous-time, the works in [23] (see also [24]) is among the first to devoted to the distributed convex optimization algorithms in continuous-time (DCO-CT), without giving proofs of algorithm convergence. Then [6] presents a proof and analyzes the distributed continuous-time convex optimization in more detail by using tools from nonsmooth analysis and set-valued dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Averaging approach to distributed convex optimization for continuous-time multi-agent systems

Ni¹,

Wang²

2017

Kybernetika

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“…In [12], Lou et al proposed an approximately projected consensus algorithm to achieve the intersection of convex sets. In [13], Wang and Elia proposed a distributed continuous-time algorithm to achieve optimization by controlling the sum of subgradients of convex functions. However, the case where the intersection set of all convex regions is empty is rarely concerned.…”

Section: Introductionmentioning

confidence: 99%

A New Algorithm for Distributed Control Problem with Shortest-Distance Constraints

Zhou

Zheng

Shen

2016

Mathematical Problems in Engineering

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This paper investigates the distributed shortest-distance problem of multiagent systems where agents satisfy the same continuoustime dynamics. The objective of multiagent systems is to find a common point for all agents to minimize the sum of the distances from each agent to its corresponding convex region. A distributed consensus algorithm is proposed based on local information. A sufficient condition also is given to guarantee the consensus. The simulation example shows that the distributed shortest-distance consensus algorithm is effective for our theoretical results.

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Control approach to distributed optimization

Cited by 294 publications

References 7 publications

Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs

Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs

Averaging approach to distributed convex optimization for continuous-time multi-agent systems

A New Algorithm for Distributed Control Problem with Shortest-Distance Constraints

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