pith. sign in

arxiv: 2604.13404 · v1 · submitted 2026-04-15 · 📡 eess.SY · cs.SY

Optimal Decentralized Dynamic Energy Management over Asynchronous Peer-to-Peer Transactive Networks via Operator Splitting

Xi Zhang , Huqiang Cheng , Guo Chen , Huaqing Li , Liang Ran , Jinhui Hu , Tingwen Huang This is my paper

Pith reviewed 2026-05-10 13:16 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords decentralized energy managementasynchronous optimizationpeer-to-peer networksoperator splittingsaddle-point problemsconvergence analysistransactive energy
0
0 comments X

The pith

Dynamic energy management over asynchronous P2P networks reaches optimal solutions via operator splitting with linear and almost-sure convergence.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper recasts a class of dynamic energy management tasks as saddle-point problems and applies operator splitting to produce two decentralized algorithms. Syn-DYNA runs synchronously and converges linearly without asymptotic qualifiers. Asyn-DYNA removes the global clock by letting agents activate randomly and maintain local buffers of the latest states, while still converging almost surely. This matters because real P2P networks with prosumers and renewables operate on irregular local timings, so removing synchronization removes a practical bottleneck while keeping optimality and privacy.

Core claim

By reformulating dynamic energy management as a saddle-point problem, the authors obtain Syn-DYNA, which delivers non-asymptotic linear convergence under synchronous updates through operator splitting, and Asyn-DYNA, which employs a random activation scheme together with local buffers to track states and establishes almost sure convergence for fully asynchronous operation over P2P transactive networks.

What carries the argument

Operator splitting on the monotone operator form of the saddle-point problem, extended by a random activation rule and local buffers that store the most recent neighbor states for Asyn-DYNA.

If this is right

  • Prosumers can coordinate energy trades and storage decisions locally without waiting for a global clock, removing synchronization delays.
  • The same framework supplies explicit linear rates for the synchronous case and almost-sure guarantees for the asynchronous case.
  • Only neighbor-to-neighbor messages and local buffers are required, preserving data privacy.
  • Numerical tests on dynamic renewable scenarios confirm that both algorithms reach the optimal operating point.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same splitting-plus-random-activation pattern could be tested on other time-varying distributed problems such as real-time market clearing or electric vehicle charging.
  • Local buffers reduce the need for continuous communication, suggesting lower bandwidth requirements in field deployments.
  • If the activation probabilities can be made event-driven rather than purely random, the method might support adaptive, low-communication triggers.

Load-bearing premise

The original energy management problem can be rewritten exactly as a saddle-point problem to which monotone operator theory applies without altering feasibility or optimality.

What would settle it

A small-scale simulation or hardware test in which Asyn-DYNA, following its stated random activation and buffer rules, repeatedly produces energy schedules whose total cost deviates from the known centralized optimum would disprove the almost-sure convergence claim.

Figures

Figures reproduced from arXiv: 2604.13404 by Guo Chen, Huaqing Li, Huqiang Cheng, Jinhui Hu, Liang Ran, Tingwen Huang, Xi Zhang.

Figure 1
Figure 1. Figure 1: A conceptual P2P trading system example management has attracted significant attention as a viable mechanism to optimize energy management [4], [5]. Char￾acterized by an open, decentralized direct trading model and high transparency, this system fundamentally shifts the trans￾action paradigm. Its core value lies in dynamically balancing local supply and demand, thereby enhancing the economic arXiv:2604.134… view at source ↗
Figure 2
Figure 2. Figure 2: Synchronous versus asynchronous updates B. Asyn-DYNA Development The implementation of Algorithm 1 relies on a global clock, which makes it only available to Syn-P2P transactive net￾works. However, in practice, there are unavoidable factors such as communication delays and idle time due to heterogenous computational capabilities of agents (prosumers’ computation units) [33]–[35]. In fact, running a synchro… view at source ↗
Figure 3
Figure 3. Figure 3: P2P communication networks. To quantify the performance of the proposed algorithms un￾der both synchronous and asynchronous schemes, we evaluate the evolution of traded power and optimal price signals during different periods, where the result related to the evolution of traded power has been deferred to Section VII-E in the sup￾plementary material for length consideration. Figs. 4-6 demon￾strate the corre… view at source ↗
Figure 4
Figure 4. Figure 4: Optimal price signal at different time for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Optimal price signal at different time for [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimal price signal at different time for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Convergence performance across different metrics. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a)-(d) show the evolution of traded power for the [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of traded power at different periods for [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of traded power at different periods for [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
read the original abstract

Peer-to-peer (P2P) energy management facilitates decentralized resource allocation among prosumers, improving local hosting capacity for renewables and minimizing energy expenditures while ensuring data privacy through distributed coordination. However, conventional P2P energy management methods are confined to synchronous scheduling paradigms, creating synchronization bottlenecks that fundamentally conflict with the dynamic and decentralized nature of P2P energy management tasks. To bridge this gap, this paper focuses on resolving a class of dynamic energy management problems over asynchronous P2P (Asyn-P2P) transactive networks. We first recast the dynamic energy management problems into a saddle-point problem, and then propose a synchronous decentralized dynamic energy management algorithm, dubbed Syn-DYNA,based on operator splitting theory. To eliminate the global synchronization clock in Syn-DYNA, we introduce a random activation scheme, together with local buffers for latest state tracking, to develop an asynchronous variant of Syn-DYNA, namely Asyn-DYNA. Based on monotone operator theory, theoretical analysis proves a non-asymptotic linear convergence rate for Syn-DYNA and establishes the almost sure convergence ofAsyn-DYNA. Numerical experiments validate effectiveness of Syn-DYNA and Asyn-DYNA algorithms by tackling a dynamic energy management task over P2P transactive networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript recasts a class of dynamic energy management problems over peer-to-peer transactive networks as saddle-point problems. It then develops a synchronous decentralized algorithm (Syn-DYNA) via operator splitting that is claimed to enjoy non-asymptotic linear convergence, and an asynchronous variant (Asyn-DYNA) that employs random activation and local buffers to achieve almost-sure convergence without a global clock. Numerical experiments are provided to illustrate performance on a dynamic energy-management task.

Significance. If the stated convergence guarantees hold under the paper's assumptions, the work supplies a practical route to decentralized, synchronization-free control for dynamic P2P energy systems. The explicit use of monotone-operator theory to obtain non-asymptotic rates (rather than merely asymptotic results) would be a useful technical contribution for the transactive-energy literature.

major comments (1)
  1. [§3 and convergence analysis] §3 (saddle-point reformulation) and the subsequent convergence theorem for Syn-DYNA: the claimed non-asymptotic linear rate requires the monotone operator to be strongly monotone (or the splitting operator to be contractive with a modulus independent of iteration). Standard P2P energy-management objectives (linear or piecewise-linear generation costs, linear network losses) produce a monotone but not strongly monotone operator. Forward-backward or Douglas-Rachford splitting then yields only sub-linear rates unless extra regularization or strong-convexity assumptions are introduced. The manuscript must either exhibit a positive strong-monotonicity modulus for the operator defined in §3 or state the additional assumptions that restore linear convergence.
minor comments (2)
  1. [Abstract] Abstract: missing space in “convergence ofAsyn-DYNA” and stray period after “Asyn-DYNA.”.
  2. [Algorithm description] Notation: the random-activation probability and buffer-update rules should be stated explicitly with symbols before the convergence proof, rather than only in the algorithm box.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback, particularly on the convergence analysis. We address the major comment point-by-point below and will revise the manuscript to strengthen the technical presentation.

read point-by-point responses

  1. Referee: §3 and convergence analysis: the claimed non-asymptotic linear rate requires the monotone operator to be strongly monotone. Standard P2P energy-management objectives (linear or piecewise-linear generation costs, linear network losses) produce a monotone but not strongly monotone operator. The manuscript must either exhibit a positive strong-monotonicity modulus for the operator defined in §3 or state the additional assumptions that restore linear convergence.

    Authors: We agree with the referee that non-asymptotic linear convergence via operator splitting (e.g., forward-backward or Douglas-Rachford) requires the monotone operator to be strongly monotone with a modulus independent of the iteration. The current manuscript states linear convergence for Syn-DYNA under the assumption that the saddle-point operator is strongly monotone, but does not explicitly link this to conditions on the cost functions. Standard linear or piecewise-linear costs indeed yield only monotonicity, resulting in sublinear rates in general. To correct this, we will revise §3 and the convergence theorem to explicitly require strong convexity of the generation and loss functions (with a uniform modulus), which ensures the desired strong monotonicity. We will also add a brief discussion noting that this assumption is standard in the literature for obtaining linear rates and can be enforced via quadratic regularization when needed. This clarifies the result's scope without changing the algorithm or the almost-sure convergence claim for Asyn-DYNA. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation begins by recasting the dynamic energy management problem as a saddle-point problem, then applies standard operator-splitting and monotone-operator results (external to the paper) to obtain the stated convergence guarantees for Syn-DYNA and Asyn-DYNA. No step reduces a claimed prediction or theorem to a quantity defined inside the paper by construction, no parameters are fitted and then relabeled as predictions, and no load-bearing uniqueness or ansatz is imported via self-citation. The analysis is self-contained against external benchmarks in monotone-operator theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the assumption that the energy-management problem admits a saddle-point formulation to which standard monotone-operator convergence theorems apply; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Dynamic energy management problems over P2P networks can be recast as saddle-point problems
    Explicitly stated as the first modeling step in the abstract.
  • standard math Monotone operator theory guarantees linear convergence for the synchronous operator-splitting algorithm and almost-sure convergence for the asynchronous variant
    Invoked for the theoretical analysis of Syn-DYNA and Asyn-DYNA.

pith-pipeline@v0.9.0 · 5549 in / 1349 out tokens · 31229 ms · 2026-05-10T13:16:00.996795+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [1]

    Peer-to-peer multi-energy trading in a decentralized network: A review,

    A. H. Tariq and U. Amin, “Peer-to-peer multi-energy trading in a decentralized network: A review,”Renewable and Sustainable Energy Reviews, vol. 208, no. 2024, p. 114969, 2025

    work page 2024

  2. [2]

    Convex opti- mization, game theory, and variational inequality theory,

    G. Scutari, D. P. Palomar, F. Facchinei, and J.-s. Pang, “Convex opti- mization, game theory, and variational inequality theory,”IEEE Signal Processing Magazine, vol. 27, no. 3, pp. 35–49, 2010

    work page 2010

  3. [3]

    Towards the next generation of smart grids: Semantic and holonic multi-agent man- agement of distributed energy resources,

    S. Howell, Y . Rezgui, J. L. Hippolyte, B. Jayan, and H. Li, “Towards the next generation of smart grids: Semantic and holonic multi-agent man- agement of distributed energy resources,”Renewable and sustainable energy reviews, vol. 77, no. 2015, pp. 193–214, 2017

    work page 2015

  4. [4]

    Vertex scenario-based robust peer-to- peer transactive energy trading in distribution networks,

    X. Chang, Y . Xu, and H. Sun, “Vertex scenario-based robust peer-to- peer transactive energy trading in distribution networks,”International Journal of Electrical Power and Energy Systems, vol. 138, no. 2021, p. 107903, 2022

    work page 2021

  5. [5]

    Prediction-based peer-to- peer energy transaction market design for smart grids,

    I. Chien, P. Karthikeyan, and P. A. Hsiung, “Prediction-based peer-to- peer energy transaction market design for smart grids,”Engineering Applications of Artificial Intelligence, vol. 126, 2023

    work page 2023

  6. [6]

    Transactive energy framework for optimal energy management of multi-carrier energy hubs under local electrical, thermal, and cooling market constraints,

    M. Khorasany, A. Najafi-Ghalelou, R. Razzaghi, and B. Mohammadi- Ivatloo, “Transactive energy framework for optimal energy management of multi-carrier energy hubs under local electrical, thermal, and cooling market constraints,”International Journal of Electrical Power and Energy Systems, vol. 129, p. 106803, 2021

    work page 2021

  7. [7]

    International journal of electrical power and energy systems a real time peer-to- peer energy trading for prosumers utilizing time-varying building virtual energy storage,

    X. Wang, H. Jia, Z. Wang, X. Jin, Y . Deng, and Y . Mu, “International journal of electrical power and energy systems a real time peer-to- peer energy trading for prosumers utilizing time-varying building virtual energy storage,”International Journal of Electrical Power and Energy Systems, vol. 155, no. PB, p. 109547, 2024

    work page 2024

  8. [8]

    User-centric Peer-to-Peer energy trading mechanisms for residential microgrids,

    S. Wu, F. Zhang, and D. Li, “User-centric Peer-to-Peer energy trading mechanisms for residential microgrids,”2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2), pp. 1–6, 2018

    work page 2018

  9. [9]

    Two-stages bidding strategies for residential microgrids based peer-to-peer energy trading,

    Z. Zhang, H. Tang, Q. Huang, and W. J. Lee, “Two-stages bidding strategies for residential microgrids based peer-to-peer energy trading,” Conference Record - Industrial and Commercial Power Systems Techni- cal Conference, vol. 2019, pp. 1–9, 2019

    work page 2019

  10. [10]

    Peer-to- peer trading in distribution systems with the utility ’s operation,

    X. Xiao, F. Wang, S. Member, M. Shahidehpour, and L. Fellow, “Peer-to- peer trading in distribution systems with the utility ’s operation,”CSEE Journal of Power and Energy Systems, vol. 10, no. 2, pp. 629–638, 2024

    work page 2024

  11. [11]

    Preserving operation privacy of peer-to-peer energy transaction based on enhanced benders decomposition considering uncertainty of renewable energy generations,

    Y . Xia, Q. Xu, S. Tao, P. Du, Y . Ding, and J. Fang, “Preserving operation privacy of peer-to-peer energy transaction based on enhanced benders decomposition considering uncertainty of renewable energy generations,”Energy, vol. 250, p. 123567, 2022

    work page 2022

  12. [12]

    Incremental cost consensus algorithm in a smart grid environment,

    Z. Zhang and M. Y . Chow, “Incremental cost consensus algorithm in a smart grid environment,”IEEE Power and Energy Society General Meeting, pp. 1–6, 2011

    work page 2011

  13. [13]

    Consensus + Innovations approach for distributed multiagent coordination in a microgrid,

    G. Hug, S. Kar, and C. Wu, “Consensus + Innovations approach for distributed multiagent coordination in a microgrid,”IEEE Transactions on Smart Grid, vol. 6, no. 4, pp. 1893–1903, 2015

    work page 1903

  14. [14]

    Distributed optimal energy management for energy internet,

    H. Zhang, Y . Li, D. W. Gao, and J. Zhou, “Distributed optimal energy management for energy internet,”IEEE Transactions on Industrial Informatics, vol. 13, no. 6, pp. 3081–3097, 2017

    work page 2017

  15. [15]

    Multiclass energy nanagement for peer-to-peer energy trading driven by prosumer preferences,

    T. Morstyn and M. D. McCulloch, “Multiclass energy nanagement for peer-to-peer energy trading driven by prosumer preferences,”IEEE Transactions on Power Systems, vol. 34, no. 5, pp. 4005–4014, 2019

    work page 2019

  16. [16]

    Impact of communication delay on asynchronous distributed optimal power flow using ADMM,

    J. Guo, G. Hug, and O. Tonguz, “Impact of communication delay on asynchronous distributed optimal power flow using ADMM,”2017 IEEE International Conference on Smart Grid Communications (SmartGrid- Comm), pp. 177–182, 2017

    work page 2017

  17. [17]

    Convergence analysis of distributed generalized Nash equilibria seeking algorithm with asynchrony and delays,

    H. Li, L. Ran, L. Zheng, Z. Li, J. Hu, J. Li, and T. Huang, “Convergence analysis of distributed generalized Nash equilibria seeking algorithm with asynchrony and delays,”IEEE Transactions on Automatic Control, vol. 70, no. 1, pp. 642–648, 2024

    work page 2024

  18. [18]

    Distributionally robust joint chance-constrained dispatch for integrated transmission-distribution systems via distributed optimization,

    J. Zhai, Y . Jiang, Y . Shi, S. Member, C. N. Jones, and X.-p. Zhang, “Distributionally robust joint chance-constrained dispatch for integrated transmission-distribution systems via distributed optimization,”IEEE Transactions on Smart Grid, vol. 13, no. 3, pp. 2132–2147, 2022

    work page 2022

  19. [19]

    Peer-to-Peer local energy trading with voltage management under asynchronous communication,

    M. H. Ullah and J. D. Park, “Peer-to-Peer local energy trading with voltage management under asynchronous communication,”IEEE Trans- actions on Smart Grid, vol. 13, no. 6, pp. 4969–4972, 2022

    work page 2022

  20. [20]

    Peer-to- Peer multi-energy trading among heterogeneous building prosumers via asynchronous distributed algorithm,

    X. Jin, X. Wang, H. Jia, Y . Mu, Q.-w. Wu, and W. Wei, “Peer-to- Peer multi-energy trading among heterogeneous building prosumers via asynchronous distributed algorithm,”IEEE Transactions on Smart Grid, vol. 16, no. 2, pp. 1590–1603, 2025

    work page 2025

  21. [21]

    An asynchronous peer-to-peer energy trading among heterogeneous low-carbon building prosumers,

    X. Wang, H. Jia, S. Member, X. Jin, Y . Mu, W. Wei, X. Yu, S. Liang, and W. Tang, “An asynchronous peer-to-peer energy trading among heterogeneous low-carbon building prosumers,”2024 IEEE Power & Energy Society General Meeting (PESGM), pp. 1–5, 2024

    work page 2024

  22. [22]

    A Byzantine- resilient distributed peer-to-peer energy management approach,

    X. Chang, Y . Xu, Q. Guo, H. Sun, and W. K. Chan, “A Byzantine- resilient distributed peer-to-peer energy management approach,”IEEE Transactions on Smart Grid, vol. 14, no. 1, pp. 623–634, 2023

    work page 2023

  23. [23]

    Multiclass energy management for peer-to-peer energy trading driven by prosumer prefer- ences,

    T. Morstyn, M. D. Mcculloch, and S. Member, “Multiclass energy management for peer-to-peer energy trading driven by prosumer prefer- ences,”IEEE Transactions on Power Systems, vol. 34, no. 5, pp. 4005– 4014, 2018

    work page 2018

  24. [24]

    A decentralized peer-to-peer energy trading strategy considering flexible resource involvement and renewable energy uncertainty,

    W. Zhou, W. Dang, F. Peng, R. Mahesuti, L. Zhang, and K. Sun, “A decentralized peer-to-peer energy trading strategy considering flexible resource involvement and renewable energy uncertainty,”International Journal of Electrical Power and Energy Systems, vol. 152, p. 109275, 2023

    work page 2023

  25. [25]

    Multi-agent systems in peer-to-peer energy trading: A comprehensive survey,

    M. I. A. Shah, A. Wahid, E. Barrett, and K. Mason, “Multi-agent systems in peer-to-peer energy trading: A comprehensive survey,”Engineering Applications of Artificial Intelligence, vol. 132, p. 107847, 2024

    work page 2024

  26. [26]

    Online distributed optimization for spatio-temporally constrained real-time peer-to-peer energy trading,

    J. Liu, Q. Long, R. P. Liu, W. Liu, and Y . Hou, “Online distributed optimization for spatio-temporally constrained real-time peer-to-peer energy trading,”Applied Energy, vol. 331, p. 120216, 2023

    work page 2023

  27. [27]

    Peer-to-peer energy trading in transactive markets considering physical network constraints,

    M. H. Ullah and J. D. Park, “Peer-to-peer energy trading in transactive markets considering physical network constraints,”IEEE Transactions on Smart Grid, vol. 12, no. 4, pp. 3390–3403, 2021

    work page 2021

  28. [28]

    Decen- tralized dual proximal gradient algorithms for non-smooth constrained composite optimization problems,

    H. Li, J. Hu, L. Ran, Z. Wang, Q. L ¨u, Z. Du, and T. Huang, “Decen- tralized dual proximal gradient algorithms for non-smooth constrained composite optimization problems,”IEEE Transactions on Parallel and Distributed Systems, vol. 32, no. 10, pp. 2594–2605, 2021

    work page 2021

  29. [29]

    Distributed dynamic pricing in peer-to-peer transactive energy systems in smart grid,

    M. H. Ullah, A. Alseyat, and J. D. Park, “Distributed dynamic pricing in peer-to-peer transactive energy systems in smart grid,” inIEEE Power and Energy Society General Meeting, 2020, pp. 1–5

    work page 2020

  30. [30]

    D. P. Bertsekas,Nonlinear programming, 2nd ed. Cambridge, MA: Athena Scientific, Cambridge, USA, 1999

    work page 1999

  31. [31]

    Latafat and P

    P. Latafat and P. Patrinos,Asymmetric forward–backward–adjoint split- ting for solving monotone inclusions involving three operators. Springer US, 2017, vol. 68, no. 1

    work page 2017

  32. [32]

    H. H. Bauschke and P. L. Combettes,Convex analysis and monotone operator theory in Hilbert spaces, 2011

    work page 2011

  33. [33]

    Asynchronous iterations in optimization: New sequence results and sharper algorithmic guarantees,

    H. R. Feyzmahdavian and M. Johansson, “Asynchronous iterations in optimization: New sequence results and sharper algorithmic guarantees,” Journal of Machine Learning Research, vol. 24, no. 158, pp. 1–75, 2023

    work page 2023

  34. [34]

    Delay-agnostic asynchronous distributed optimization,

    X. Wu, C. Liu, S. Magn ´usson, and M. Johansson, “Delay-agnostic asynchronous distributed optimization,” inProceedings of the IEEE Conference on Decision and Control, 2023, pp. 1082–1087

    work page 2023

  35. [35]

    Achieving linear con- vergence in distributed asynchronous multiagent optimization,

    Y . Tian, Y . Sun, G. Scutari, and S. Member, “Achieving linear con- vergence in distributed asynchronous multiagent optimization,”IEEE Transactions on Automatic Control, vol. 65, no. 12, pp. 5264–5279, 2020

    work page 2020

  36. [36]

    Distributed energy resource coordination over time-varying directed communication networks,

    T. Yang, D. Wu, H. Fang, W. Ren, H. Wang, Y . Hong, and K. H. Johansson, “Distributed energy resource coordination over time-varying directed communication networks,”IEEE Transactions on Control of Network Systems, vol. 6, no. 3, pp. 1124–1134, 2019

    work page 2019

  37. [37]

    P. L. Combettes,Quasi-Fej ´erian analysis of some optimization algo- rithms. Elsevier Masson SAS, 2001, vol. 8

    work page 2001

  38. [38]

    Decentralized consensus optimization with asynchrony and delays,

    T. Wu, K. Yuan, Q. Ling, W. Yin, and A. H. Sayed, “Decentralized consensus optimization with asynchrony and delays,”IEEE Transactions on Signal and Information Processing over Networks, vol. 4, no. 2, pp. 293–307, 2018

    work page 2018

  39. [39]

    ARock: An algorithmic frame- work for asynchronous parallel coordinate updates,

    Z. Peng, Y . Xu, M. Yan, and W. Yin, “ARock: An algorithmic frame- work for asynchronous parallel coordinate updates,”SIAM Journal on Scientific Computing, vol. 38, no. 5, pp. A2851—-A2879, 2016

    work page 2016

  40. [40]

    Optimization over time-varying networks and unbounded information delays,

    A. Ramaswamy, A. Redder, and D. E. Quevedo, “Optimization over time-varying networks and unbounded information delays,”IEEE Trans- actions on Automatic Control, vol. 67, no. 8, pp. 4131–4137, 2022

    work page 2022

  41. [41]

    Delay- adaptive distributed stochastic optimization,

    Z. Ren, Z. Zhou, L. Qiu, A. Deshpande, and J. Kalagnanam, “Delay- adaptive distributed stochastic optimization,”AAAI 2020 - 34th AAAI Conference on Artificial Intelligence, pp. 5503–5510, 2020

    work page 2020

  42. [42]

    Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time,

    J. Peypouquet and S. Sorin, “Evolution equations for maximal monotone operators: asymptotic analysis in continuous and discrete time,”Journal of Convex Analysis, vol. 17, no. 3-4, pp. 1113–1163, 2010. 1 VII. SUPPLEMENTARYMATERIAL A. Proof of Lemma 2 Recalling the update rule (22), we have U k+1 −U ∗ 2 Ts − U k −U ∗ 2 Ts =− U k+1 −U k 2 Ts + 2 U k+1 −U ∗ ⊤...

    work page 2010