The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Zero-Gradient-Sum Algorithms for Distributed Convex Optimization: The Continuous-Time Case
Abstract
This technical note presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponentially, and obtain lower and upper bounds on their convergence rates in terms of the network topologies, problem characteristics, and algorithm parameters, including the algebraic connectivity, Laplacian spectral radius, and function curvatures. The findings of this technical note may be regarded as a natural generalization of several well-known algorithms and results for distributed consensus, to distributed convex optimization.
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Cites
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Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
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BackgroundConsensus seeking in multiagent systems under dynamically changing interaction topologies
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Distributed Subgradient Methods for Multi-Agent Optimization
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Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization
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Cited by
A survey of distributed optimization
Yang, T., Yi, X., Wu, J., Yuan, Y., Wu, D., Meng, Z., Hong, Y., Wang, H., Lin, Z., & Johansson, K. H. (2019) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2019.05.006 · Cited by 913
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Lin, P., Ren, W., & Farrell, J. A. (2017) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2016.2604324 · Cited by 403
A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization
Liu, Q., & Wang, J. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2015.2416927 · Cited by 397
Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs
Nedic, A., & Olshevsky, A. (2014) · arXiv · doi:10.48550/arxiv.1406.2075 · Cited by 38
Metadata
- Authors
- Lu, J., & Tang, C. Y.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2012-09
- Volume
- 57
- Issue
- 9
- Pages
- 2348-2354
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2571423792
- Cited by
- 403
- References
- 19
- FWCI
- 10.97
- Type
- journal article
- Language
- en
- Open access
- closed
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