Convergence rate for consensus with delays
Integrity signals
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Under Assumptions 6 and 7, for B satisfying B ≥ B⊖ and the stated conditions, for any k ≥ B-1 and any matrix b, if a = R~^B(k)b, then ||a||_L ≤ δ||b||_L.
“Lemma 13 ( B -step consensus contraction ). Under Assumptions 6 and 7, let B be an integer satisfying B ≥ B ⊖ and such that”
From Achieving Geometric Convergence for Distributed Optimization Over Time-Varying Graphs (2017) · cites this paper as [48]
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“≥ Based on those bounds on C ij ( k ), v j ( k ), and 1 /v i ( k + 1), we can have the following equivalent arc-utilization lower bound Thus, we have where the second inequality comes from Lemma 5 of reference [48].”
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- Authors
- Nedić, A., & Ozdaglar, A.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Massachusetts Institute of Technology (US)
- Corresponding author
- Nedić, Angelia
- Venue
- Journal of Global Optimization
- Published
- 2008-11-04
- Volume
- 47
- Issue
- 3
- Pages
- 437-456
- ISSN
- 0925-5001 (ISSN-L)
- 1573-2916
- OpenAlex
- W2093777540
- Cited by
- 198
- References
- 23
- Citations by year
- 2026: 3 · 2025: 9 · 2024: 10 · 2023: 13 · 2022: 4 · 2021: 13 · 2020: 13 · 2019: 14 · 2018: 16 · 2017: 14 · 2016: 8 · 2015: 14 · 2014: 15 · 2013: 12 · 2012: 12
- FWCI
- 15.33
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Global Optimization (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
- Physical Sciences › Computer Science › Computer Networks and Communications › Neural Networks Stability and Synchronization
- Keywords
- consensus algorithms, multi-agent systems, time-varying connectedness, communication delay, convergence rate, asynchronous operation, bounded delay
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