Subgradient methods and consensus algorithms for solving convex optimization problems

By Björn Johansson, Tamás Keviczky, Mikael Johansson, Karl Henrik Johansson. IEEE Conference on Decision and Control, 2008

311 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/9bb91a2d6ef9bf643a6253da85739dbc5677da63

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Citations in the corpus

On the O(1=k) convergence of asynchronous distributed alternating Direction Method of Multipliers (2013, background): “3 Several follow-up papers considered variants of this metho d for problems with local and global constraints [26], [36] ra ndomly varying networks [29], [30], [31] and random gradient errors [42], [34].”
Distributed Continuous-Time Convex Optimization With Time-Varying Cost Functions (2015, methodology): “For example, this combination is used in [4] for solving the coupled optimization problems with a fixed undirected graph.”
Distributed multi-task classification: a decentralized online learning approach (2017, methodology): “Incremental methods [5,7,25] require the network to form a special ring and transmit the updated information through a cyclic trajectory one after the other, while consensus methods [14,19,23] require each node to perform two updating steps: it first aggregates the iterates from its direct neighbors”
A gossip algorithm for convex consensus optimization over networks (2010, background): “Furthermore, the algorithms mostly assume delay- and error-free communications with no quantization over directed graphs, although there are a few exceptions: [18] allowed the presence of bounded time delays, [28] considered random additive errors in subgradient evaluations, [20], [26] studied the e”
Adaptation, Learning, and Optimization over Networks (2014, background): “, [18, 26, 32, 46, 84, 87, 128, 138, 139, 175, 176, 186, 199, 205, 209, 215, 225, 242, 243, 266, 268]; (c) diffusion strategies — see, e.”
Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs (2014, methodology): “Our work here contributes to the growing literature on distributed methods for optimization over networks [5], [9], [12], [14]–[16], [19]–[23], [28], [32], [34], [40], [43].”
Distributed Constrained Optimization by Consensus-Based Primal-Dual Perturbation Method (2013, background): “Contributions: Different from the existing works [9]–[14] where the local v ariable constraints are usually simple (in the sense that they can be handled via s imple projection) and independent among agents, in this paper, we consider a problem formulati on that has a general set of convex inequalit”
Balancing Communication and Computation in Distributed Optimization (2017, background): “A number of later contributions [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] extended DGD to other settings, including stochastic networks, constrained problems, and noisy environments.”
Decentralized Online Learning With Kernels (2017, methodology): “Therefore, we adopt an approximate primalonly approach based on penalty methods [32], [33], which in decentralized optimization is known as distributed gradient descent (DGD).”
Distributed dual averaging method for multi-agent optimization with quantized communication (2012, methodology): “There has been much recent research interest in developing distributed methods for solving convex optimization problems in networked-systems [1–7].”
Adaptive Networks (2014, background): “…time scale for performing multiple consensus iterations similar to (54b) over the states of the neighbors, and a second slower time scale for performing gradient vector updates or for updating the estimators by using the result of the consensus iterations (e.g., [81], [87], [89], and [106]–[109]).”
Diffusion Strategies Outperform Consensus Strategies for Distributed Estimation Over Adaptive Networks (2012, methodology): “Original implementations of the consensus strategy relied on the use of two time-scales [20]–[22]: one tim -scale for the collection of measurements across the nodes and another time-scale to iterate sufficien tly ough over the collected data to attain agreement before the process is repeated.”
Asynchronous gossip algorithms for stochastic optimization (2009, methodology): “, [16], [18], [21], [22], [25], [27], [28]).”
A survey of distributed optimization (2019, background): “The authors of Johansson, Ke-viczky, Johansson, and Johansson (2008) modiﬁed of the DGD algo-rithm (2) by changing the order in which the consensus-step and the subgradient descent step are executed.”