A Distributed ADMM-like Method for Resource Sharing over Time-Varying Networks

Aybat, Necdet Serhat; Hamedani, Erfan Yazdandoost

doi:10.1137/17m1151973

Cited by 30 publications

(23 citation statements)

References 25 publications

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“…However, the work in [36] requires an assumption of strict convexity of the objective functions, whereas in [11] it is assumed only that the functions are convex. We also note some related work is presented in [3], [4], in which distributed primal-dual methods with conic constraints are considered.…”

Section: A Related Workmentioning

confidence: 99%

Distributed resource allocation on dynamic networks in quadratic time

Doan

Olshevsky

2017

Systems & Control Letters

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We consider the problem of allocating a fixed amount of resource among nodes in a network when each node suffers a cost which is a convex function of the amount of resource allocated to it. We propose a new deterministic and distributed protocol for this problem. Our main result is that the associated convergence time for the global objective scales quadratically in the number of nodes on any sequence of time-varying undirected graphs satisfying a long-term connectivity condition.

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Section: A Related Workmentioning

confidence: 99%

Distributed resource allocation on dynamic networks in quadratic time

Doan

Olshevsky

2017

Systems & Control Letters

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“…This rate is further improved in [6] by optimizing its dependence on the number of nodes. In addition, there are also several ADMM based methods that only work on balanced networks [7]- [9]. By exploiting the mirror relationship between the distributed optimization and distributed resource allocation, several accelerated distributed resource allocation algorithms are given in [10].…”

Section: A Literature Reviewmentioning

confidence: 99%

“…However, its convergence rate is unclear if either the strongly convexity or the Lipschitz smoothness is removed. In [9], a push-sum based algorithms is given in tie with the ADMM. Although it can handle time-varying networks, the convergence rate is O(1/k) even for strongly convex and Lipschitz smooth functions.…”

Section: A Literature Reviewmentioning

confidence: 99%

Distributed Dual Gradient Tracking for Resource Allocation in Unbalanced Networks

Zhang

You

Cai

2020

IEEE Trans. Signal Process.

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This paper proposes a distributed conjugate gradient tracking algorithm (DCGT) to solve resource allocation problems in a possibly unbalanced network, where each node of the network computes its optimal resource via interacting only with its neighboring nodes. Our key idea is the novel use of the celebrated AB algorithm to the dual of the resource allocation problem. To study the convergence of DCGT, we first establish the sublinear convergence of AB for non-convex objective functions, which advances the existing results on AB as they require the strong-convexity of objective functions. Then we show that DCGT converges linearly for strongly convex and Lipschitz smooth objective functions, and sublinearly without the Lipschitz smoothness. Finally, simulation results validate that DCGT outperforms state-of-the-art algorithms in distributed resource allocation problems.

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“…However, such algorithms with vanishing step sizes cannot be extended to handle problems with timevarying objectives and usually exhibits poor convergence. A recent work [11] has proposed a class of algorithms to handle the resource sharing problem under the conic constraints. The algorithms are built on a modified Lagrangian function and an ADMM-like scheme for seeking a saddle point of the Lagrangian function, which has been shown to have an ergodic O(1/k) rate for agents' objective functions and constraints violation.…”

Section: A Literature Reviewmentioning

confidence: 99%

“…The algorithms are built on a modified Lagrangian function and an ADMM-like scheme for seeking a saddle point of the Lagrangian function, which has been shown to have an ergodic O(1/k) rate for agents' objective functions and constraints violation. The problem formulation in [11] treats (1) as a special case: the constraint (1b) is replaced by the more general on consensus and push-sum approaches [12], a recent reference [13] proposes a distributed algorithm for solving problem (1) over time-varying directed networks and provides convergence guarantees. Aside from the above algorithms which are all discrete-time methods, there are some continuous-time algorithms such as the one in reference [14], where convergence under general convexity assumption is ensured.…”

Section: A Literature Reviewmentioning

confidence: 99%

Improved Convergence Rates for Distributed Resource Allocation

Nedić

Olshevsky

Shi

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper, we develop a class of decentralized algorithms for solving a convex resource allocation problem in a network of n agents, where the agent objectives are decoupled while the resource constraints are coupled. The agents communicate over a connected undirected graph, and they want to collaboratively determine a solution to the overall network problem, while each agent only communicates with its neighbors. We first study the connection between the decentralized resource allocation problem and the decentralized consensus optimization problem. Then, using a class of algorithms for solving consensus optimization problems, we propose a novel class of decentralized schemes for solving resource allocation problems in a distributed manner. Specifically, we first propose an algorithm for solving the resource allocation problem with an o(1/k) convergence rate guarantee when the agents' objective functions are generally convex (could be nondifferentiable) and per agent local convex constraints are allowed; We then propose a gradient-based algorithm for solving the resource allocation problem when per agent local constraints are absent and show that such scheme can achieve geometric rate when the objective functions are strongly convex and have Lipschitz continuous gradients. We have also provided scalability/network dependency analysis. Based on these two algorithms, we have further proposed a gradient projectionbased algorithm which can handle smooth objective and simple constraints more efficiently. Numerical experiments demonstrates the viability and performance of all the proposed algorithms. DRAFT n i=1 (R i x i − r i ) ∈ K where K is a convex cone and R i is a matrix that couples local resources. It was required that the interior of K is nonempty which does not apply to (1b).The authors recently removed such nonempty interior requirement on K during our preparation of this paper. We also would like to point out that our rates are non-ergodic and the measures/criteria used for our rates have some advantages in practical uses (see the comments following Theorem 2). Based December 18, 2018 DRAFT

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A Distributed ADMM-like Method for Resource Sharing over Time-Varying Networks

Cited by 30 publications

References 25 publications

Distributed resource allocation on dynamic networks in quadratic time

Distributed resource allocation on dynamic networks in quadratic time

Distributed Dual Gradient Tracking for Resource Allocation in Unbalanced Networks

Improved Convergence Rates for Distributed Resource Allocation

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