Distributed Optimization and Games: A Tutorial Overview

Yang, Bo; Johansson, Mikael

doi:10.1007/978-0-85729-033-5_4

Cited by 74 publications

(75 citation statements)

References 55 publications

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“…We can observe from Figures 1(a)-(b) that, for the proposed distributed PDP method, the instantaneous iterates oscillate and may not be feasible (they are nearly feasible though); whereas the running average iterates are always feasible but converge slower. From Figure 1(a), we also observe that the proposed distributed PDP method converges faster than the distributed PD method in [9] and the distributed dual subgradient method in [13]. In Figure 1(c), we further present the optimal regression solution of (13) (obtained by CVX) and that obtained by the proposed distributed PDP method (at iteration 10, 000).…”

Section: Numerical Example and Discussionmentioning

confidence: 64%

“…Note that, for (13), the associated proximal perturbation point in (10a) has a close-form solution similar to the soft thresholding operator in (8), and, thus, it is easy to implement. In addition to the proposed PDP method, we also implemented the distributed (consensus-based) PD subgradient method in [9] (which does not have the perturbation point) as well as the distributed (consensus-based) dual subgradient method [13] for comparison 1 . We evaluated the normalized accuracy at each iteration k, defined as (C(x (k) ) −C ⋆ )/C ⋆ , whereC ⋆ denotes the optimal value of (13) obtained by the (centralized) convex solver CVX [16].…”

Section: Numerical Example and Discussionmentioning

confidence: 97%

“…In addition, we computed the constraint feasibility, Figure 1 displays the simulation results. The step size was set to ak = 10/(100 + k) for the distributed PD method in [9] and to ak = 0.2/(50 + k) for the distributed dual subgradient method in [13]; while ak = 0.1/(10 + k), ρ1 = 0.5 and ρ2 = 0.5 were set for the proposed distributed PDP method. Note that these parameters were manually set so that each of the methods can respectively exhibit best convergence results.…”

Section: Numerical Example and Discussionmentioning

confidence: 99%

“…In contrast to the dual optimization method [8,13] where one has to globally solve the inner minimization problem min x∈X L(x, λ) at each iteration, the primal-dual (PD) subgradient method [11] can handle (2) with lower complexity. Specifically, at each iteration k, the PD subgradient method performs one primal subgradient update and one dual subgradient update, respectively:…”

Section: Network Model and Problem Statementmentioning

confidence: 99%

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Distributed sparse regression by consensus-based primal-dual perturbation optimization

Chang

Nedić

Scaglione

2013

2013 IEEE Global Conference on Signal and Information Processing

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This paper studies the decentralized solution of a multi-agent sparse regression problem in the form of a globally coupled objective function with a non-smooth sparsity promoting constraint. In particular, we propose a distributed primal-dual perturbation (PDP) method which combines the average consensus technique and the primaldual perturbed subgradient method. Compared to the conventional primal-dual (PD) subgradient method without perturbation, the PDP subgradient method exhibits a faster convergence behavior. In order to handle the non-smooth constraints, we propose a novel proximal gradient type perturbation point. The proposed distributed optimization algorithm can be implemented as a fully decentralized protocol, with each agent using its local information and exchanging messages between neighbors only. We show that the proposed method converges to the global optimum of the considered problem under standard convex problem and network assumptions.

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Section: Numerical Example and Discussionmentioning

confidence: 64%

Section: Numerical Example and Discussionmentioning

confidence: 97%

Section: Numerical Example and Discussionmentioning

confidence: 99%

Section: Network Model and Problem Statementmentioning

confidence: 99%

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Distributed sparse regression by consensus-based primal-dual perturbation optimization

Chang

Nedić

Scaglione

2013

2013 IEEE Global Conference on Signal and Information Processing

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“…Broadcasting Δ (a ( )) = 0 to ∀ ∈ ; Sending ← to the system; (13) END IF (14) END WHILE Algorithm 1: Synchronous distributed algorithm (SDA).…”

Section: Theorem 16mentioning

confidence: 99%

Game-Theoretic Based Distributed Scheduling Algorithms for Minimum Coverage Breach in Directional Sensor Networks

Yue

Liu

et al. 2014

International Journal of Distributed Sensor Networks

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A directional sensor network, where a lot of sensors are intensively and randomly deployed, is able to enhance coverage performances, since working directions can be partitioned into different K covers which are activated in a round-robin fashion. In this paper, we consider the problem of direction set K-Cover for minimum coverage breach in directional sensor networks. First, we formulate the problem as a game called direction scheduling game (DSG), which we prove as a potential game. Thus, the existence of pure Nash equilibria can be guaranteed, and the optimal coverage is a pure Nash equilibrium, since the potential function of DSGs is consistent with the coverage objective function of the underlying network. Second, we propose the synchronous and asynchronous game-theoretic based distributed scheduling algorithms, which we prove to converge to pure Nash equilibria. Third, we present the explicit bounds on the coverage performance of the proposed algorithms by theoretical analysis of the algorithms' coverage performance. Finally, we show experimental results and conclude that the Nash equilibria can provide a near-optimal and well-balanced solution.

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Distributed hybrid impulsive algorithm with supervisory resetting for nonlinear optimization problems

Xia

Zeng

Sun

et al. 2021

Intl J Robust & Nonlinear

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A distributed impulsive algorithm is presented for solving large‐scale nonlinear optimization problems, which is based on state‐dependent impulsive dynamical system theory. The optimization problem, whose objective function is a sum of convex and continuously differentiable functions, is solved over a multi‐agent network system. The proposed algorithm takes distributed updates in continuous‐time part and centralized updates in discrete‐time part, which can improve the convergence performance. With stability theory of impulsive dynamical systems, the proposed impulsive algorithm is proved to converge to one optimal solution, and under certain conditions, agents' states are proved to converge at a linear convergence rate. In numerical simulation, compared with conventional distributed continuous‐time algorithm, the performance advantage of the proposed impulsive method is demonstrated.

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Distributed Optimization and Games: A Tutorial Overview

Cited by 74 publications

References 55 publications

Distributed sparse regression by consensus-based primal-dual perturbation optimization

Distributed sparse regression by consensus-based primal-dual perturbation optimization

Game-Theoretic Based Distributed Scheduling Algorithms for Minimum Coverage Breach in Directional Sensor Networks

Distributed hybrid impulsive algorithm with supervisory resetting for nonlinear optimization problems

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