pith. sign in

arxiv: 2605.20638 · v1 · pith:JJI3RDSRnew · submitted 2026-05-20 · 🧮 math.OC · cs.SY· eess.SY

Distributed and Decentralized Optimization Algorithms via Consensus ALADIN

Xu Du , Jingzhe Wang , Karl H. Johansson , Apostolos I. Rikos This is my paper

Pith reviewed 2026-05-21 04:17 UTC · model grok-4.3

classification 🧮 math.OC cs.SYeess.SY
keywords distributed optimizationconsensus optimizationALADIN algorithmdecentralized optimizationquantized communicationconvergence guaranteesdirected graphsnon-convex optimization
0
0 comments X

The pith

Consensus ALADIN extends ALADIN to directly solve distributed consensus optimization with global convergence for convex problems and local convergence for non-convex ones.

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

The paper develops Consensus ALADIN, or C-ALADIN, as an extension of the ALADIN framework tailored for consensus constraints in distributed optimization. It includes first-order and second-order variants that use Hessian approximations to limit information exchange. A decentralized implementation is introduced for operation over directed graphs using quantized communication and finite-time coordination protocols. The methods come with global convergence guarantees when the problem is convex and local guarantees otherwise, with the decentralized version approaching the solution within a quantization-dependent neighborhood. This matters for applications such as smart grids and machine learning where optimization must occur across networked agents with limited communication.

Core claim

C-ALADIN directly handles consensus constraints within the augmented Lagrangian-based alternating direction inexact Newton framework. It offers a first-order variant and a second-order variant that employs a Hessian approximation to avoid transmitting second-order information. The decentralized variant operates over directed graphs with quantized communication via a finite-time coordination protocol. Both versions guarantee global convergence for convex problems and local convergence for non-convex problems, while the decentralized iterates converge to a neighborhood of the optimum whose size is determined by the quantization level.

What carries the argument

Consensus ALADIN (C-ALADIN), which augments the ALADIN method to incorporate consensus constraints directly and uses finite-time coordination for decentralization over quantized directed graphs.

If this is right

  • The first- and second-order variants substantially reduce communication and computational costs relative to prior decentralized methods.
  • Global convergence holds for convex objective functions under the stated conditions.
  • Local convergence is guaranteed for non-convex problems near the solution.
  • The decentralized version converges to an optimum neighborhood bounded by the quantization level.
  • Fast local convergence is preserved despite the approximations and decentralization.

Where Pith is reading between the lines

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

  • If the finite-time coordination protocol succeeds, the approach could apply to other networked systems with directed topologies and bandwidth limits.
  • Quantization level acts as a tunable parameter balancing accuracy and communication overhead in practical deployments.
  • Hybrid methods combining C-ALADIN with event-triggered or asynchronous updates may further reduce resource use in dynamic environments.
  • Scalability to very large networks could be tested by applying the algorithm to distributed training tasks in machine learning.

Load-bearing premise

The finite-time coordination protocol must be realizable over the directed graph with the specified quantized communication to ensure the neighborhood convergence in the decentralized case.

What would settle it

A simulation on a directed graph with quantization levels too coarse for the coordination protocol to achieve consensus within the assumed bounds, showing whether the iterates remain within the predicted neighborhood or diverge.

Figures

Figures reproduced from arXiv: 2605.20638 by Apostolos I. Rikos, Jingzhe Wang, Karl H. Johansson, Xu Du.

Figure 1
Figure 1. Figure 1: Comparison of convergence performance among Pull￾FTERC [21], AsyAD-ADMM [55], QuAsyADMM [44], the proposed first￾order C-ALADIN (12), and its quantized decentralized version (27) under different quantization levels ∆ = 10−4, 10−5, 10−6 [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence Algorithm 4among Algorithm 1, the first-order C-ALADIN in (12), its quantized decentralized version (27), and the decentralized approximate second-order C-ALADIN (Algorithm 4) under different quantization levels ∆ = 10−4, 10−5, 10−6. 0 50 100 150 10-8 10-6 10-4 10-2 100 102 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Convergence comparison among Algorithm 1, Algorithm 3 with ∆ = 10−9, and GIANT [22]. of the inner consensus QP solver; therefore, only the case with ∆ = 10−9 is shown. In this setting, Algorithm 3 converges nearly as fast as Algorithm 1, reaching a neighborhood of the optimal solution. For comparison, the centralized GIANT method, which is based on primal decomposition, is included. B. Non-convex Case For … view at source ↗
read the original abstract

Distributed optimization has found widespread applications in smart grids, optimal control, and machine learning. This paper studies distributed consensus optimization. We extend the Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) framework to propose Consensus ALADIN (C-ALADIN) with a central coordinator, which directly handles consensus constraints. Our C-ALADIN algorithm admits both a first-order variant and a second-order variant that employs a Hessian approximation, avoiding direct transmission of second-order information while preserving fast local convergence. We then develop a decentralized version of C-ALADIN that operates over directed graphs with quantized communication, using a finite-time coordination protocol. For both versions, we establish global convergence guarantees for convex problems and local convergence guarantees for non-convex problems. For the decentralized case, the iterates converge to a neighborhood of the optimum determined by the quantization level. Numerical results demonstrate that our methods retain fast convergence while substantially reducing communication and computational costs compared to existing decentralized approaches.

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 extends the ALADIN framework to Consensus ALADIN (C-ALADIN) for distributed consensus optimization problems. It introduces a centralized coordinator version with both first-order and second-order variants (the latter using a Hessian approximation to avoid transmitting second-order information), followed by a decentralized variant that operates over directed graphs using quantized communication and a finite-time coordination protocol. Global convergence guarantees are established for convex problems and local convergence guarantees for non-convex problems; in the decentralized case the iterates are shown to converge to a neighborhood of the optimum whose size is determined by the quantization level. Numerical results are presented to demonstrate retained fast convergence with reduced communication and computational costs relative to existing decentralized methods.

Significance. If the stated convergence guarantees hold under the paper's assumptions, the work provides a useful extension of ALADIN-type methods to consensus-constrained problems with practical communication constraints. The combination of a Hessian-approximation second-order variant, quantization, and a finite-time protocol on directed graphs addresses real constraints in applications such as smart grids and networked control, while the numerical comparisons illustrate concrete efficiency gains. The explicit neighborhood result for the quantized decentralized case is a concrete, falsifiable prediction that strengthens the contribution.

major comments (1)
  1. [§5.3] §5.3 (Decentralized convergence analysis) and the finite-time coordination protocol description: the neighborhood convergence claim for the decentralized iterates depends on the protocol achieving the required approximate consensus in finite time on a directed graph under uniform quantization. Standard finite-time consensus results on directed graphs require strong connectivity together with weight-balancing or push-sum mechanisms; persistent bounded quantization errors can prevent exact finite-time termination or inflate the effective neighborhood. The manuscript does not explicitly verify that the protocol construction satisfies these conditions while preserving the ALADIN update structure, which is load-bearing for the decentralized guarantee.
minor comments (2)
  1. [Abstract] The abstract states that the methods 'substantially reduc[e] communication and computational costs' but does not name the specific baseline algorithms used in the numerical comparison; adding this would improve clarity.
  2. [Section 2] Notation for the consensus constraint and the quantization operator is introduced without a dedicated table or summary; a short notation table would aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript extending the ALADIN framework to consensus optimization problems. We address the major comment point by point below and have made revisions to improve the clarity of the decentralized analysis.

read point-by-point responses

  1. Referee: [§5.3] §5.3 (Decentralized convergence analysis) and the finite-time coordination protocol description: the neighborhood convergence claim for the decentralized iterates depends on the protocol achieving the required approximate consensus in finite time on a directed graph under uniform quantization. Standard finite-time consensus results on directed graphs require strong connectivity together with weight-balancing or push-sum mechanisms; persistent bounded quantization errors can prevent exact finite-time termination or inflate the effective neighborhood. The manuscript does not explicitly verify that the protocol construction satisfies these conditions while preserving the ALADIN update structure, which is load-bearing for the decentralized guarantee.

    Authors: We thank the referee for highlighting this important aspect of the analysis. Upon review, we acknowledge that the original manuscript could benefit from a more explicit verification of the protocol's properties. In the revised manuscript, we have added a new paragraph in §5.3 that explicitly states the assumptions on the directed graph (strong connectivity and the use of a weight-balancing or push-sum mechanism as per standard finite-time consensus protocols). We verify that under uniform quantization, the protocol achieves approximate consensus in finite time, with the approximation error bounded by the quantization level. This bounded error is then incorporated into the convergence analysis as a perturbation, preserving the ALADIN update structure and leading to convergence to a neighborhood of the optimum. We believe this addition addresses the concern while maintaining the integrity of the decentralized version. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper extends the existing ALADIN framework to C-ALADIN for direct handling of consensus constraints, introduces first- and second-order variants, and develops a decentralized version via a finite-time coordination protocol on directed graphs with quantization. Global convergence for convex problems and local convergence for non-convex problems, with neighborhood size determined by quantization level, are established through standard analysis of the algorithm iterates and protocol properties rather than by redefinition, fitting to the target result, or load-bearing self-citation chains. No equations or steps reduce the claimed guarantees to inputs by construction; the work remains self-contained against external benchmarks from optimization theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions from distributed optimization literature such as convexity or smoothness of local objective functions and the existence of a finite-time coordination protocol under quantization.

axioms (2)
  • domain assumption Local objective functions are convex (for global convergence) or twice continuously differentiable (for local convergence)
    Invoked to establish the stated convergence guarantees for the C-ALADIN variants.
  • domain assumption A finite-time coordination protocol exists over the directed graph with quantized communication
    Required for the neighborhood convergence result in the decentralized case.

pith-pipeline@v0.9.0 · 5708 in / 1359 out tokens · 28900 ms · 2026-05-21T04:17:43.281822+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages · 6 internal anchors

  1. [1]

    Distributed consensus optimization with consensus ALADIN,

    X. Du and J. Wang, “Distributed consensus optimization with consensus ALADIN,” in 2025 American Control Conference (ACC) , 2025, pp. 2949–2955

    work page 2025

  2. [2]

    Decentralized optim ization via RC-ALADIN with efficient quantized communication,

    X. Du, K. H. Johansson, and A. I. Rikos, “Decentralized optim ization via RC-ALADIN with efficient quantized communication,” in 2025 IEEE 64th Conference on Decision and Control (CDC) . IEEE, 2025, p. 4357–4363

    work page 2025

  3. [3]

    Dec entral- ized real-time iterations for distributed NMPC,

    G. Stomberg, A. Engelmann, M. Diehl, and T. Faulwasser, “Dec entral- ized real-time iterations for distributed NMPC,” IEEE Transactions on Automatic Control, 2025

    work page 2025

  4. [4]

    Dis- tributed real-time cooperative model predictive control,

    Y . Jiang, K. Fedorov´ a, R. Schwan, J. Oravec, and C. N. Jones, “Dis- tributed real-time cooperative model predictive control, ” IEEE Transac- tions on Automatic Control , 2026

    work page 2026

  5. [5]

    A time splittin g based optimization method for nonlinear MHE,

    S. Wu, Y . Wang, J. Wang, A. I. Rikos, and X. Du, “A time splittin g based optimization method for nonlinear MHE,” in 2025 IEEE 64th Confer- ence on Decision and Control (CDC) . IEEE, 2025, p. 5335–5341

    work page 2025

  6. [6]

    Preconditioned inexact stochastic ADMM for deep models,

    S. Zhou, O. Wang, Z. Luo, Y . Zhu, and G. Y . Li, “Preconditioned inexact stochastic ADMM for deep models,” Nature Machine Intelligence , pp. 1–12, 2026

    work page 2026

  7. [7]

    Federated learning via inexact ADMM,

    S. Zhou and G. Y . Li, “Federated learning via inexact ADMM,” IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 45, no. 8, pp. 9699–9708, 2023

    work page 2023

  8. [8]

    Distributed Energy System Design including Unbalanced AC Power Flow for Large LV Networks with ADMM

    R. Steven, O. V . Klymenko, and M. Short, “Distributed energy system design including unbalanced AC power flow for large L V networ ks with ADMM,” arXiv preprint arXiv:2605.04746 , 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  9. [9]

    Dis- tributed state estimation for AC power systems using Gauss- Newton ALADIN,

    X. Du, A. Engelmann, Y . Jiang, T. Faulwasser, and B. Houska, “ Dis- tributed state estimation for AC power systems using Gauss- Newton ALADIN,” in 58th Conference on Decision and Control (CDC) , 2019, pp. 1919–1924

    work page 2019

  10. [10]

    Survey of distr ibuted algorithms for resource allocation over multi-agent syste ms,

    M. Doostmohammadian, A. Aghasi, M. Pirani, E. Nekouei, H. Za rrabi, R. Keypour, A. I. Rikos, and K. H. Johansson, “Survey of distr ibuted algorithms for resource allocation over multi-agent syste ms,” Annual Reviews in Control , vol. 59, p. 100983, 2025. AUTHOR et al.: TITLE 15

    work page 2025

  11. [11]

    Distributed optimization and statistical learning via the alternating direction method of multipliers,

    S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al. , “Distributed optimization and statistical learning via the alternating direction method of multipliers,” F oundations and Trends® in Machine learning , vol. 3, no. 1, pp. 1–122, 2011

    work page 2011

  12. [12]

    Notes on de compo- sition methods,

    S. Boyd, L. Xiao, A. Mutapcic, and J. Mattingley, “Notes on de compo- sition methods,” Notes for EE364B, Stanford University , vol. 635, pp. 1–36, 2007

    work page 2007

  13. [13]

    Quantized z eroth- order gradient tracking algorithm for distributed nonconv ex optimization under polyak–łojasiewicz condition,

    L. Xu, X. Yi, C. Deng, Y . Shi, T. Chai, and T. Y ang, “Quantized z eroth- order gradient tracking algorithm for distributed nonconv ex optimization under polyak–łojasiewicz condition,” IEEE Transactions on Cybernetics, vol. 54, no. 10, pp. 5746–5758, 2024

    work page 2024

  14. [14]

    Distributed subgradient methods for multi- agent optimization,

    A. Nedic and A. Ozdaglar, “Distributed subgradient methods for multi- agent optimization,” IEEE Transactions on Automatic Control , vol. 54, no. 1, pp. 48–61, 2009

    work page 2009

  15. [15]

    EXTRA: An exact first-order algorithm for decentralized consensus optimization,

    W. Shi, Q. Ling, G. Wu, and W. Yin, “EXTRA: An exact first-order algorithm for decentralized consensus optimization,” SIAM Journal on Optimization, vol. 25, no. 2, pp. 944–966, 2015

    work page 2015

  16. [16]

    Batch normalization: Acceleratin g deep network training by reducing internal covariate shift,

    S. Ioffe and C. Szegedy, “Batch normalization: Acceleratin g deep network training by reducing internal covariate shift,” in International conference on machine learning . pmlr, 2015, pp. 448–456

    work page 2015

  17. [17]

    Communication-efficient learning of deep networks from de centralized data,

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from de centralized data,” in Artificial intelligence and statistics . PMLR, 2017, pp. 1273– 1282

    work page 2017

  18. [18]

    Nesterov Accelerated Distributed Optimization with Efficient Quantized Communication

    R. Wu, X. Du, K. H. Johansson, and A. I. Rikos, “Nesterov accel erated distributed optimization with efficient quantized communi cation,” arXiv preprint arXiv:2604.16906, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  19. [19]

    Distributed consensus of li near multi- agent systems with adaptive dynamic protocols,

    Z. Li, W. Ren, X. Liu, and L. Xie, “Distributed consensus of li near multi- agent systems with adaptive dynamic protocols,” Automatica, vol. 49, no. 7, pp. 1986–1995, 2013

    work page 1986

  20. [20]

    Push–pull gradient metho ds for distributed optimization in networks,

    S. Pu, W. Shi, J. Xu, and A. Nedi´ c, “Push–pull gradient metho ds for distributed optimization in networks,” IEEE Transactions on Automatic Control, vol. 66, no. 1, pp. 1–16, 2020

    work page 2020

  21. [21]

    A fast finite-time consensus b ased gradient method for distributed optimization over digraph s,

    W. Jiang and T. Charalambous, “A fast finite-time consensus b ased gradient method for distributed optimization over digraph s,” in 2022 IEEE 61st Conference on Decision and Control (CDC) . IEEE, 2022, pp. 6848–6854

    work page 2022

  22. [22]

    Giant: Globally improved approximate newton method for distributed optimi zation,

    S. Wang, F. Roosta, P . Xu, and M. W. Mahoney, “Giant: Globally improved approximate newton method for distributed optimi zation,” Advances in Neural Information Processing Systems , vol. 31, 2018

    work page 2018

  23. [23]

    A Newton tracking algorit hm with exact linear convergence for decentralized consensus optimization,

    J. Zhang, Q. Ling, and A. M.-C. So, “A Newton tracking algorit hm with exact linear convergence for decentralized consensus optimization,” IEEE Transactions on Signal and Information Processing over Networks, vol. 7, pp. 346–358, 2021

    work page 2021

  24. [24]

    Incremental quasi-Newton a lgorithms for solving a nonconvex, nonsmooth, finite-sum optimizatio n problem,

    G. Dinc Y alcin and F. E. Curtis, “Incremental quasi-Newton a lgorithms for solving a nonconvex, nonsmooth, finite-sum optimizatio n problem,” Optimization Methods and Software , vol. 39, no. 2, pp. 345–367, 2024

    work page 2024

  25. [25]

    Decomposition principle for lin ear pro- grams,

    G. B. Dantzig and P . Wolfe, “Decomposition principle for lin ear pro- grams,” Operations research, vol. 8, no. 1, pp. 101–111, 1960

    work page 1960

  26. [26]

    An augmented Lagrangian based algorithm for distributed nonconvex optimization,

    B. Houska, J. Frasch, and M. Diehl, “An augmented Lagrangian based algorithm for distributed nonconvex optimization,” SIAM Journal on Optimization, vol. 26, no. 2, pp. 1101–1127, 2016

    work page 2016

  27. [27]

    Distributed optimization and contr ol with ALADIN,

    B. Houska and Y . Jiang, “Distributed optimization and contr ol with ALADIN,” Recent Advances in Model Predictive Control: Theory, Algorithms, and Applications , pp. 135–163, 2021

    work page 2021

  28. [28]

    DLM: Decentralized li nearized alternating direction method of multipliers,

    Q. Ling, W. Shi, G. Wu, and A. Ribeiro, “DLM: Decentralized li nearized alternating direction method of multipliers,” IEEE Transactions on Signal Processing, vol. 63, no. 15, pp. 4051–4064, 2015

    work page 2015

  29. [29]

    Passivity-based interpret ation of the Tracking-ADMM algorithm for distributed constraint-coup led optimiza- tion,

    I. Notarnicola and A. Falsone, “Passivity-based interpret ation of the Tracking-ADMM algorithm for distributed constraint-coup led optimiza- tion,” in 2025 IEEE 64th Conference on Decision and Control (CDC) . IEEE, 2025, pp. 3983–3988

    work page 2025

  30. [30]

    Affine-coupled Distributed Optimization via Distributed Proximal Jacobian ADMM with Quantized Communication

    X. Du, B. Han, I. Notarnicola, K. H. Johansson, and A. I. Rikos, “Affine-coupled distributed optimization via distr ibuted proxi- mal Jacobian ADMM with quantized communication,” arXiv preprint arXiv:2604.14861, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  31. [31]

    Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers

    X. Wang, M. Hong, S. Ma, and Z.-Q. Luo, “Solving multiple-blo ck separable convex minimization problems using two-block al ternating direction method of multipliers,” arXiv preprint arXiv:1308.5294 , 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  32. [32]

    Nocedal and S

    J. Nocedal and S. Wright, Numerical optimization . Springer Science & Business Media, New Y ork, 2006

    work page 2006

  33. [33]

    Toward distributed OPF using ALADIN,

    A. Engelmann, Y . Jiang, T. M¨ uhlpfordt, B. Houska, and T. Fau lwasser, “Toward distributed OPF using ALADIN,” IEEE Transactions on Power Systems, vol. 34, no. 1, pp. 584–594, 2019

    work page 2019

  34. [34]

    Decomposition of non-convex optimization via bi-level distributed ALADI N,

    A. Engelmann, Y . Jiang, B. Houska, and T. Faulwassser, “Decomposition of non-convex optimization via bi-level distributed ALADI N,” IEEE Transactions on Control of Network Systems , vol. 7, no. 4, pp. 1848– 1858, 2020

    work page 2020

  35. [35]

    ALADIN- β : A distributed optimization algorithm for solving MPCC prob lems,

    Y . Wang, S. Wu, G. Y ang, J. Chu, A. I. Rikos, and X. Du, “ALADIN- β : A distributed optimization algorithm for solving MPCC prob lems,” in 2025 IEEE 64th Conference on Decision and Control (CDC) . IEEE, 2025, pp. 5329–5334

    work page 2025

  36. [36]

    Consensus ALADIN: A framework for distrib uted optimization and its application in federated learning,

    X. Du and J. Wang, “Consensus ALADIN: A framework for distrib uted optimization and its application in federated learning,” arXiv preprint arXiv:2306.05662, 2023

    work page arXiv 2023

  37. [37]

    Convergence theory of flexible ALADIN for distributed optimization,

    X. Du, X. Zhou, S. Zhu, and A. I. Rikos, “Convergence theory of flexible ALADIN for distributed optimization,” in 2025 European Control Conference (ECC) . IEEE, 2025, pp. 1907–1912

    work page 2025

  38. [38]

    A bi-level globalization strat- egy for non-convex consensus ADMM and ALADIN,

    X. Du, J. Wang, X. Zhou, and Y . Mao, “A bi-level globalization strat- egy for non-convex consensus ADMM and ALADIN,” arXiv preprint arXiv:2309.02660, 2023

    work page arXiv 2023

  39. [39]

    Mix-CALADIN: A Distributed Algorithm for Consensus Mixed-Integer Optimization

    B. Han, X. Du, K. H. Johansson, and A. I. Rikos, “Mix-CALADIN: A distributed algorithm for consensus mixed-integer optimi zation,” arXiv preprint arXiv:2604.14897, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  40. [40]

    Distributed MPC with ALADIN- a tutoria l,

    B. Houska and J. Shi, “Distributed MPC with ALADIN- a tutoria l,” in 2022 American Control Conference (ACC) . IEEE, 2022, pp. 358–363

    work page 2022

  41. [41]

    Lightweight Real-Time ALADIN for Distributed Optimization

    Y . Wang, X. Feng, S. Pan, L. Zhu, X. Du, and A. I. Rikos, “Lightweight real-time ALADIN for distributed optimizati on,” arXiv preprint arXiv:2604.15176, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  42. [42]

    Partially distributed outer approximation,

    A. Murray, T. Faulwasser, V . Hagenmeyer, M. Villanueva, and B. Houska, “Partially distributed outer approximation,” Journal of Global Optimization , vol. 80, pp. 523–550, 2021

    work page 2021

  43. [43]

    Learning (with) distributed optimization,

    A. Aadhithya A, V . Radhakrishnan et al. , “Learning (with) distributed optimization,” arXiv e-prints , pp. arXiv–2308, 2023

    work page 2023

  44. [44]

    Asyn- chronous distributed optimization via ADMM with efficient c ommuni- cation,

    A. I. Rikos, W. Jiang, T. Charalambous, and K. H. Johansson, “ Asyn- chronous distributed optimization via ADMM with efficient c ommuni- cation,” in IEEE Conference on Decision and Control , 2023, pp. 7002– 7008

    work page 2023

  45. [45]

    Nonlinear co nsensus protocols with applications to quantized communication an d actuation,

    J. Wei, X. Yi, H. Sandberg, and K. H. Johansson, “Nonlinear co nsensus protocols with applications to quantized communication an d actuation,” IEEE Transactions on Control of Network Systems , vol. 6, no. 2, pp. 598–608, 2019

    work page 2019

  46. [46]

    IQN: An incremental q uasi- Newton method with local superlinear convergence rate,

    A. Mokhtari, M. Eisen, and A. Ribeiro, “IQN: An incremental q uasi- Newton method with local superlinear convergence rate,” SIAM Journal on Optimization , vol. 28, no. 2, pp. 1670–1698, 2018

    work page 2018

  47. [47]

    Kovalev, K

    D. Kovalev, K. Mishchenko, and P . Richt´ arik, “Stochastic N ewton and cubic Newton methods with simple local linear-quadratic ra tes,” arXiv preprint arXiv:1912.01597, 2019

    work page arXiv 1912

  48. [48]

    Lecture notes on numerical optimization,

    M. Diehl, “Lecture notes on numerical optimization,” University of Freiburg, Freiburg, 2016

    work page 2016

  49. [49]

    Sun and Y .-X

    W. Sun and Y .-X. Y uan, Optimization theory and methods: nonlinear programming. Springer Science & Business Media, 2006, vol. 1

    work page 2006

  50. [50]

    Proximal ADMM for nonconvex and nonsmooth optimization,

    Y . Y ang, Q.-S. Jia, Z. Xu, X. Guan, and C. J. Spanos, “Proximal ADMM for nonconvex and nonsmooth optimization,” Automatica, vol. 146, p. 110551, 2022

    work page 2022

  51. [51]

    H. K. Khalil, Nonlinear control. Pearson New Y ork, 2015, vol. 406

    work page 2015

  52. [52]

    Beck, First-order methods in optimization

    A. Beck, First-order methods in optimization . SIAM, 2017

    work page 2017

  53. [53]

    Structure-exploiting model predictive control for real-time and embedded applications,

    K. Fedorov´ a, “Structure-exploiting model predictive control for real-time and embedded applications,” Ph.D. dissertation, 2025. [On line]. Avail- able: https://www.uiam.sk/assets/publication info.php?id pub=2723

    work page 2025

  54. [54]

    Non-osc illating quantized average consensus over dynamic directed topolog ies,

    A. I. Rikos, C. N. Hadjicostis, and K. H. Johansson, “Non-osc illating quantized average consensus over dynamic directed topolog ies,” Auto- matica, vol. 146, p. 110621, 2022

    work page 2022

  55. [55]

    An asynchronous approximate distributed alternating direct ion method of multipliers in digraphs,

    W. Jiang, A. Grammenos, E. Kalyvianaki, and T. Charalambous , “An asynchronous approximate distributed alternating direct ion method of multipliers in digraphs,” in IEEE Conference on Decision and Control , 2021, pp. 3406–3413

    work page 2021

  56. [56]

    Dis- tributed optimization with gradient descent and quantized communica- tion,

    A. I. Rikos, W. Jiang, T. Charalambous, and K. H. Johansson, “ Dis- tributed optimization with gradient descent and quantized communica- tion,” IF AC-PapersOnLine, vol. 56, no. 2, pp. 5900–5906, 2023

    work page 2023

  57. [57]

    Distributed optimization via gradient descent with ev ent-triggered zooming over quantized communication,

    ——, “Distributed optimization via gradient descent with ev ent-triggered zooming over quantized communication,” in IEEE Conference on Deci- sion and Control , 2023, pp. 6321–6327

    work page 2023

  58. [58]

    Distributed optimization with finite bit adaptive quan tization for efficient communication and precision enhancement,

    ——, “Distributed optimization with finite bit adaptive quan tization for efficient communication and precision enhancement,” in IEEE Confer- ence on Decision and Control , 2024, pp. 2531–2537

    work page 2024

  59. [59]

    CasADi – a software framework for nonlinear optimization a nd optimal control,

    J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. D iehl, “CasADi – a software framework for nonlinear optimization a nd optimal control,” Mathematical Programming Computation , vol. 11, no. 1, pp. 1–36, 2019

    work page 2019

  60. [60]

    Numerical analysis (nineth ed ition),

    R. L. Burden and J. D. Faires, “Numerical analysis (nineth ed ition),” Thomson Brooks/Cole, pp. 57–58, 2010

    work page 2010