Dual decomposition for multi-agent distributed optimization with coupling constraints

Falsone, Alessandro; Margellos, Konstantinos Nektarios; Garatti, Simone; Prandini, Maria

doi:10.1016/j.automatica.2017.07.003

Cited by 177 publications

(208 citation statements)

References 30 publications

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“…A time-varying distributed algorithm based on Fenchel duality is provided in [136]. Papers [137,96] investigate distributed dual subgradient methods for constraint-coupled optimization. In [138] an ADMM approach for the same set-up is proposed in which multiple consensus steps are needed.…”

Section: Discussion and Referencesmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

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The presence of embedded electronics and communication capabilities as well as sensing and control in smart devices has given rise to the novel concept of cyber-physical networks, in which agents aim at cooperatively solving complex tasks by local computation and communication. Numerous estimation, learning, decision and control tasks in smart networks involve the solution of large-scale, structured optimization problems in which network agents have only a partial knowledge of the whole problem. Distributed optimization aims at designing local computation and communication rules for the network processors allowing them to cooperatively solve the global optimization problem without relying on any central unit. The purpose of this survey is to provide an introduction to distributed optimization methodologies. Principal approaches, namely (primal) consensus-based, duality-based and constraint exchange methods, are formalized. An analysis of the basic schemes is supplied, and state-of-the-art extensions are reviewed.

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Section: Discussion and Referencesmentioning

confidence: 99%

“…A proof of the statement is provided in [96] for time-varying networks using a proximal minimization perspective. Notice that Theorem 23 does not state any convergence property for the primal variables x t i .…”

Section: Algorithm 5 Distributed Dual Subgradientmentioning

confidence: 99%

Distributed Optimization for Smart Cyber-Physical Networks

Notarstefano¹,

Notarnicola²,

Camisa³

2019

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“…Consider the electric vehicle charging control problem as presented in [27], [28]; an alternative formulation is considered in [5]. The problem consists of finding an optimal overnight charging schedule for a fleet of m vehicles, whose consumption is denoted by x i , i = 1, .…”

Section: Interpretation In Electric Vehicle Charging Controlmentioning

confidence: 99%

Linear programs for resource sharing among heterogeneous agents: The effect of random agent arrivals

Falsone

Margellos

Garatti

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-We consider a multi-agent resource sharing problem that can be represented by a linear program. The amount of resource to be shared is fixed, and each agent adds to the linear cost and constraint a term that depends on some randomly extracted parameters, thus modelling heterogeneity among agents. We study the probability that the arrival of a new agent does not affect the optimal value and the resource share of the other agents, which means that the system cannot accommodate the request of a further agent and has reached its saturation limit. In particular, we determine the maximum number of requests for the shared resource that the system can accommodate in a probabilistic sense. This result is proven by first formulating the dual of the resource sharing linear program, and then showing that this is a random linear program. Using results from the scenario theory for randomized optimization, we bound the probability of constraint violation for the dual optimal solution, and prove that this is equivalent with the primal optimal value and resource share remaining unchanged upon arrival of a new agent. We discuss how this can be thought of as probabilistic sensitivity analysis and offer an interpretation of this setting in an electric vehicle charging control problem.

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“…We note that in [23], [24], convergence is proven for agent dynamics with vanishing step sizes, which slows down the convergence rate and prevents the protocols to be translated into a continuous-time counterpart, as usual for example in power systems [1], [2], [25], [26].…”

Section: Introductionmentioning

confidence: 99%

“…Multi-agent convex constrained optimization has been considered in [22], under the assumption of uniformly bounded subgradients, and either homogeneous constraint sets or time-invariant, complete communication graph with uniform weights; in [23] under the assumption of differentiable cost functions with Lipschitz continuous and uniformly bounded gradients; and in [24]. We note that in [23], [24], convergence is proven for agent dynamics with vanishing step sizes, which slows down the convergence rate and prevents the protocols to be translated into a continuous-time counterpart, as usual for example in power systems [1], [2], [25], [26].…”

Section: Introductionmentioning

confidence: 99%

Proximal Dynamics in Multiagent Network Games

Grammatico

2018

IEEE Trans. Control Netw. Syst.

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Abstract-We consider dynamics and protocols for agents seeking an equilibrium in a network game with proximal quadratic cost coupling. We adopt an operator theoretic perspective to show global convergence to a network equilibrium, under the assumption of convex cost functions with proximal quadratic couplings, time-invariant and time-varying communication graph along with convex local constraints, and time-invariant communication graph along with convex local constraints and separable convex coupling constraints. We show that proximal dynamics generalize opinion dynamics in social networks and are applicable to distributed tertiary control in power networks. Advantageously, distributed computation and communication setups allow each agent to keep its own data private and exchange information with selected agents only. Typically, in networked multi-agent systems, the state (or decision) variables of each agent evolve as a result of local decision making, e.g. local optimization subject to private constraints, and distributed communication with some other agents, according to a communication graph. It then follows naturally that the aim of the agents is to reach a collective equilibrium state, where no agent can benefit from updating its state variables. I. INTRODUCTIONLiterature overview: In this paper, we study network games with proximal, hence quadratic, cost coupling between neighboring agents, that are related to the literature of distributed multi-agent equilibrium seeking in network games and distributed multi-agent optimization.Network games among agents with convex compact local constraints have been considered in [14] under the assumption of strongly convex quadratic cost functions and time-invariant communication graph; in [15] [16], under the assumption of differentiable cost functions with Lipschitz continuous gradient, strictly monotone pseudo-gradient game mapping (hence strictly convex cost functions), and undirected, possibly time-varying, communication graph. Multi-agent games with convex compact local and also coupling constraints have been considered in [17] under the assumption of strongly convex twice differentiable cost functions with bounded gradients, with strictly increasing congestion cost term.

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Dual decomposition for multi-agent distributed optimization with coupling constraints

Cited by 177 publications

References 30 publications

Distributed Optimization for Smart Cyber-Physical Networks

Distributed Optimization for Smart Cyber-Physical Networks

Linear programs for resource sharing among heterogeneous agents: The effect of random agent arrivals

Proximal Dynamics in Multiagent Network Games

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