Distributed Optimization Method Based On Optimal Control

Huanshui Zhang; Liping Zhang; Yeming Xu; Yue Sun; Ziyuan Guo

REVIEW 5 major objections 8 minor 27 references

Distributed Optimization Method Based On Optimal Control

T0 review · 5 major / 8 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that distributed optimization can be recast as an optimal control problem, and that the resulting algorithms converge superlinearly to the global minimizer of a sum of strongly convex functions.

desk verdict Reasonable optimal-control framing for distributed optimization, but the central superlinear proof has an algebraic error and the algorithms largely reduce to the authors' prior work. read the letter →

arxiv 2411.10658 v2 pith:BU26P6JE submitted 2024-11-16 math.OC

Ziyuan Guo , Yue Sun , Yeming Xu , Liping Zhang , Huanshui Zhang This is my paper · ORCID

classification math.OC MSC 90C2593A1649K1568W1590C53

keywords distributedoptimizationoptimalcontrolmaximumprinciplesuperlinearconvergencemulti-agentconsensusaveragegradientsecond-orderconvex

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish a new route to distributed optimization: instead of tuning step sizes and inverting Hessians, each agent treats its update as a control input and the overall task as an optimal control problem. Applying the maximum principle to the resulting multi-agent system yields an iterative algorithm, DOAOC, whose error contracts as $\|x(k+1)-x^*\| \le r_2 c^k \|x(k)-x^*\|$ with $c=\|I-\eta h^*\|<1$. Because $c^k \to 0$ geometrically, the method is superlinear: the contraction ratio shrinks on every step. A central-server variant, DOCMC, is given the same treatment with a similar bound. If these claims hold, distributed optimization over balanced, strongly connected networks can reach the optimal value at a rate usually reserved for Newton-type methods, without ever forming the inverse Hessian.

What carries the argument

The machinery is a discrete-time linear system $x(k+1)=x(k)+u(k)$ combined with a per-agent cost that penalizes consensus errors $e_{ij}(k)=x_i(k)-x_j(k)$, control effort, and the local objective $f_i$. The maximum principle turns this into forward-backward equations whose solution is the controller (12), with a Riccati equation (11) carrying the consensus information. A matrix $M(l)$ appearing in the controller is shown to converge to $\frac{1}{n}\mathbf{1}\mathbf{1}^T$, so the optimal control naturally uses the average gradient. The non-causal future-dependent controller is converted, via Lemma 3, into the iterative updates (19) and then (22), where the averaged Hessian $h(k)=\frac{1}{n}\sum_i \nabla^2 f_i(x_i(k))$ plays the role of second-order information and a scalar $\eta$ replaces the inverse matrix. This replacement is what yields the contraction factor $(I-\eta h^*)^k$ in Theorem 2.

What would settle it

Take a two-agent balanced strongly connected graph, choose strongly convex quadratics with known minimizer $x^*$, pick $\eta$ satisfying the theorem's condition, and record the ratios $\|x(k+1)-x^*\|/\|x(k)-x^*\|$ along DOAOC iterations. The theorem predicts these ratios are bounded by $r_2 c^k$, so the logarithm of the ratio should fall off linearly with $k$; observing ratios that stay bounded away from zero, or divergence for an $\eta$ inside the stated range, would disprove the central claim.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the maximum principle applied to the consensus-plus-optimization cost functional (8) produces controllers whose limiting form uses the average gradient and average Hessian, and that the non-causal controller (12) can be converted into a causal, implementable iteration. The result is an algorithm that updates each agent by $x_i(k+1)=x_i(k)+d^k_i(k)$, where each inner loop step is $d^{l+1}_i(k)=d^l_i(k)-\eta g_i(k)-\eta h_i(k)d^l_i(k)$ and the initial direction uses the consensus error. Theorem 2 states that under strong convexity and smoothness assumptions and with $\eta$ chosen so $\|I-\eta h^*\|<1$, any convergent run satisfies $\|x(k+1)-x^*\| \le r_2 c^k \|x(k)-x^*\|$, i.e. superlinear convergence, because the prefactor $c^k$ forces the contraction ratio to zero as $k$ grows.

Load-bearing premise

The superlinear claim rests on Lemma 3, which converts the maximum-principle controller into the implementable iteration; the paper does not prove this conversion but imports it from earlier work, and it is not shown that the conversion remains valid when consensus error terms are present.

Editorial extensions

If this is right

If the superlinear bound is correct, agents reach the global minimizer of (1) with a contraction ratio that itself decays geometrically, so the number of accurate digits grows at least linearly with iterations.
Because the algorithm avoids Hessian inversion, per-iteration cost stays close to gradient-type methods while the convergence rate approaches Newton-type behavior.
The consensus error term in the control law means the algorithm can tolerate agents' states being unequal, whether from initialization or communication disturbances, without losing the optimization objective.
The DOCMC central-server variant provides the same superlinear guarantee for parameter-server architectures, making the result portable to machine-learning deployments that already use a central node.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The theorem's condition $\|I-\eta h^*\|<1$ is an asymptotic condition at the optimum; the authors do not give a practical rule for selecting $\eta$ before knowing $h^*$, so a line search or adaptive estimate would be needed in applications.
Because DOAOC uses only the average Hessian through consensus, the method could plausibly be combined with finite-time average consensus protocols; the convergence proof would then need to account for the transient consensus error, a testable extension the paper does not address.
The proof structure suggests the superlinear rate is inherited from the centralized Algorithm II of the cited prior work, with the consensus term acting as a stabilizer; if that is so, improving the centralized inner loop would immediately improve the distributed algorithm.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Thanks for passing along 2411.10658. My short take: the paper's central superlinear claims don't hold as written, but the framework isn't empty.

What's actually new: the paper recasts distributed optimization as a discrete-time optimal control problem and uses the discrete maximum principle to derive second-order iterations that avoid Hessian inversion. Lemma 1's derivation of the Riccati-based controller is standard but clean, and Lemma 2's observation that the non-causal controller averages gradients is a useful connection to consensus protocols. The authors also deserve credit for being transparent about lineage: Remarks 4 and 5 say explicitly that when agent states coincide, recursions (21) and (23) reduce to Algorithms I and II from the authors' own [14] and [23]. So the genuinely new algorithmic piece is the consensus-error feedback term B^T P e(k) in the distributed setting. That's a modest but real contribution.

The problems are load-bearing. Theorem 2's proof for DOAOC has a concrete algebra error. The paper defines G = I - (ηh* + B^T P B), but the factor that actually appears in the line before (39) is I - η(h* + B^T P B); the displayed factorization only works if B^T P B = 0. The same proof replaces d_k(x(k)) by its first-order Taylor expansion about x* without bounding the remainder uniformly in k, and d_k is built from up to k inner recursions, so the remainder isn't clearly negligible. Also, c = ||I - ηh*|| < 1 does not follow from 0 < η < 1 alone; the correct sufficient condition is η < 2/m2. Theorem 1 has the same uncontrolled Taylor issue. Lemma 3, the key bridge from the non-causal controller to the implementable iteration, is deferred to [14] without a proof here, and Lemma 4's consensus proof is compressed and leans on "[23]". The text says numerical examples appear in Section V, but the version I read ends at the conclusions—no experiments.

So the superlinear convergence advertised in the title is not established. The idea might be salvageable: fix the G definition, add a genuine uniform bound on the Taylor remainder, and provide experiments. As is, I couldn't rely on the results.

My verdict: reject, but with encouragement to resubmit after fixing proofs and adding experiments. It's a borderline desk reject; I'd only send it out if you expect the authors to engage seriously with referees. I wouldn't cite it in current form. Good reading-group material for spotting proof gaps.

Referee Report

5 major / 8 minor

Summary. The paper proposes two distributed optimization algorithms, DOCMC and DOAOC, by reformulating the minimization of an average of strongly convex smooth local objective functions as a discrete-time optimal control problem. The DOCMC algorithm uses a parameter server and requires inversion of a matrix that combines the Hessian and a Riccati-term; the DOAOC algorithm replaces that inverse by a scalar step η and relies only on neighbor communication plus average-consensus evaluations of the gradient and Hessian. The paper claims convergence for DOCMC and superlinear convergence for both DOCMC (Theorem 1) and DOAOC (Theorem 2).

Significance. If the superlinear claims were rigorously established, the DOAOC algorithm would be a notable contribution: it is a distributed second-order-type method that avoids Hessian inversion, uses only a scalar step η, and has an error bound whose contraction factor decays as c^k. The algorithmic construction is clearly motivated, and the authors are explicit about connections to their prior work. However, the proof of the central superlinear result contains a concrete algebraic error and an uncontrolled Taylor approximation, the key transformation in Lemma 3 is deferred to unpublished prior work, and the consensus argument in Lemma 4 is not rigorous. These issues leave the main claims unproved in the present form.

major comments (5)

[IV, proof of Theorem 2, Eq. (39)] The factorization in Eq. (39) is algebraically incorrect. The paper defines G = I - (ηh* + B^T P B), but the displayed equality requires G = I - η(h* + B^T P B). Direct algebra gives (I - ηh*)^{k+1} - η(I - ηh*)^k B^T P B = (I - ηh*)^k [I - η(h* + B^T P B)], not (I - ηh*)^k [I - (ηh* + B^T P B)]. The claimed factorization holds only in the trivial case B^T P B = 0. Since the superlinear contraction bound r2 c^k depends on this factorization, Theorem 2 is not proved.
[IV, proof of Theorem 2, Eqs. (37)-(39)] The proof replaces the direction d̄_k(x(k)) by its first-order Taylor expansion about x* and writes '≈' in Eq. (39), but no bound on the Taylor remainder is provided. The map d̄_k depends on k through up to k inner recursions, so the remainder can in principle depend on k and may destroy the claimed c^k contraction. This is not a removable notational shortcut: the polynomial (I - ηh*)^k is exactly the source of the superlinear factor, and an uncontrolled remainder could contain terms that are not dominated by c^k.
[IV, statement of Theorem 2] The condition 'selecting 0 < η < 1 and c = ||I - ηh*|| < 1' is not sufficient as stated. Under Assumption 2, the Hessian h* satisfies m1 I ≤ h* ≤ m2 I, and the standard sufficient condition for ||I - ηh*|| < 1 is 0 < η < 2/m2, which is not implied by η < 1 when m2 > 2. The theorem statement should state the correct step-size condition and the proof should verify it; the present condition is inadequate.
[III-B, Lemma 3 and Remark 5] The central transformation from the non-causal optimal controller (12) to the implementable iteration (19) is not proved in this paper; the proof of Lemma 3 says only 'referring to [14]'. Likewise, Lemma 4 imports the convergence of the centralized subproblem from Lemma 2 of [23], and Remark 5 states that (23) is exactly Algorithm II in [23]. Since [14], [22], and [23] are preprint references and the distributed extension is the claimed contribution, these deferred arguments are load-bearing. The paper needs either self-contained proofs of these steps or a precise statement of which properties of the prior work are used and a verification that they continue to hold in the presence of the consensus terms.
[IV, Lemma 4] The consensus claim (26) is not established. Equation (25) mixes a matrix expression involving ((Γ_P + h(k))^{-1}Γ_P)^{k+1}Γ_P^{-1} L̄ with the vector x(k), and the passage to W = I - εL̄ 'satisfying the properties of P_ε in [20]' is not justified. The matrix L̄ = B^T P B R^{-1} is asserted to be a Laplacian, and the matrix ((Γ_P + h(k))^{-1}Γ_P)^{k+1} is asserted to be symmetric, but neither assertion is proved, and the cited properties in [20] require conditions that are not verified here. Thus the contraction in (26) does not follow from the displayed derivation.

minor comments (8)

[III-C heading] The heading 'Dissussion of the DOCMC and DOAOC Algorithm' contains a typo and should read 'Discussion'.
[Algorithm 1, Step 8] The loop body in Step 8 has a duplicated line number '8:' inside the for loop, which makes the pseudocode confusing.
[Abstract] The phrase 'convergence and superlinear convergence rate are also analyzed stringently' is grammatically awkward; the manuscript would benefit from a language edit throughout.
[IV, Theorem 1, Eqs. (29)-(30)] The display of Eq. (29) breaks the norm inequality across a line with the multiplication sign '(30)' on the following line; this should be formatted as a single chain of inequalities.
[IV, Eq. (27)] In Eq. (27), the factor ((Γ_P + h(k))^{-1}R)^{k+1} appears, but the derivation and surrounding text suggest it should be ((Γ_P + h(k))^{-1}Γ_P)^{k+1}. Please correct the typo.
[IV, Lemma 4] The notation x̄(k) is used before it is defined. The later definition x̄(k) = (1/n)11^T x(k) should be introduced before the inequality in (25).
[V, Conclusions] The conclusion states 'global superlinear convergence', but the theorems only provide a local contraction bound under the condition that the iterates converge. The qualifier 'local' or 'under convergence' should be added.
[I, Introduction] The introduction announces numerical examples in Section V, but no numerical section appears in the manuscript text; either include the experiments or remove the announcement.

Circularity Check

2 steps flagged · score 4.0 of 10

Heavy load-bearing self-citation: Lemma 3 and the convergence proofs are deferred to the authors' prior preprints [14] and [23].

self citation load bearing [Section III.B, Lemma 3 (proof paragraph)]
"For controller (12), noting that it exhibits non-causality because the future average gradient is used. Fortunately, the problem of utilizing the future information has been previously addressed in our research referring to [14] for the details. In accordance with the methodology presented in [14], controller (12) will transform into dk as depicted in (19)."

Lemma 3 is the sole bridge between the optimal-control solution (12) and the implementable iteration (19) on which all subsequent theorems rest. Its proof is not given; it is asserted that the non-causal controller transforms into the implementable form by the methodology of [14], a preprint by the same research group. The distributed consensus term B^T P e(k) is carried into (19) without derivation. Consequently, the claimed derivation from the maximum principle is imported from the authors' own prior work, and the convergence results inherit whatever validity [14] has.
self citation load bearing [Section IV, proof of Lemma 4]
"which is consistent with the form of Algorithm 1 in [23]. Thus, there holds F (y(k + 1)) − F (x∗) ≤ c(F (y(k)) − F (x∗)). where 0 ≤ c < 1. More details can refer to the proof of Lemma 2 in [23]."

The convergence proof for the distributed DOCMC algorithm reduces to the centralized Algorithm 1 of [23], also by the same authors. The key contraction inequality is not proved in this paper; the reader is directed to 'the proof of Lemma 2 in [23]'. Without that imported lemma, the proof of Lemma 4 does not establish convergence. Thus the paper's main convergence claim is load-bearing on a self-citation rather than a self-contained argument.

full rationale

The paper is not circular in a definitional or fitted-input sense: no parameter is fitted and the distributed algorithms contain a genuinely additional consensus/error term B^T P e(k) beyond the prior centralized algorithms. However, the derivation chain is heavily self-referential. Lemma 3, which converts the non-causal optimal controller (12) into the implementable iteration (19), is asserted solely by reference to the authors' previous work [14], with no proof supplied; the distributed consensus term is carried into (19) without derivation. Lemma 4 and Theorem 1 then reduce the convergence analysis to Algorithm 1 / Lemma 2 of [23], another preprint from the same group, using 'More details can refer to' instead of a self-contained proof. These self-citations are load-bearing because the claimed maximum-principle derivation and the convergence rates inherit their validity from [14] and [23]. Separately, the factorization in (39) of Theorem 2 appears algebraically inconsistent unless B^T P B = 0; that is a correctness risk rather than a circularity and is not reflected in the circularity score. Score 4 reflects partial, not total, circularity: the central claim is not merely a restatement of the inputs, but its derivation is not self-contained.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper's algorithm and proof rely on several unproved or deferred assumptions: the stabilizing Riccati solution, the imported transformation from [14], and the convergence lemma from [23]. The design parameters η, R, Q, H are chosen by hand and the convergence conditions reference them but do not provide concrete choices.

free parameters (3)

η = 0 < η < 1, also η < 2/m2
Scalar step size replacing the inverse matrix; Theorem 2 requires it to satisfy bounds that depend on the unknown smoothness constant m2.
R = positive definite, unspecified
Lemma 4 requires R to be 'selected appropriately' for convergence; no explicit construction or rule is given.
Q, H = positive semidefinite
Consensus weighting matrices in the cost function; their choice determines the Riccati stabilizing solution P and hence the algorithm.

assumptions (5)

domain assumption Assumption 1: The directed graph G is balanced and strongly connected.
Used throughout to ensure consensus and average computation.
domain assumption Assumption 2: Each fi is twice continuously differentiable with m1 I ≤ ∇² fi(x) ≤ m2 I for all x.
Needed for convergence analysis; implies strong convexity and smoothness.
ad hoc to paper Existence of a stable solution P of the Riccati equation (11).
Lemma 2 assumes 'If the Riccati equation (11) admits a stable solution P when k → ∞'; this existence is not proven for the given Q, H, R.
standard math The discrete-time maximum principle from [18] yields costate equations (9)-(10).
Standard external theorem; applied without proof to the specific problem.
domain assumption The superlinear convergence of the centralized algorithm in [23, Lemma 2] is imported without proof.
The paper says 'More details can refer to the proof of Lemma 2 in [23]' in Theorem 1.

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Cite this review

Pith. "Pith review of Distributed Optimization Method Based On Optimal Control." pith.science (2026). https://pith.science/paper/BU26P6JE

@misc{pith2026241110658,
  author       = {Pith},
  title        = {Pith review of: Distributed Optimization Method Based On Optimal Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BU26P6JE}},
  note         = {Machine review of arXiv:2411.10658}
}

read the original abstract

In this paper, a novel distributed optimization framework has been proposed. The key idea is to convert optimization problems into optimal control problems where the objective of each agent is to design the current control input minimizing the original objective function of itself and updated size for the future time instant. Compared with the existing distributed optimization problem for optimizing a sum of convex objective functions corresponding to multiple agents, we present a distributed optimization algorithm for multi-agents system based on the results from the maximum principle. Moreover, the convergence and superlinear convergence rate are also analyzed stringently.

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Reference graph

Works this paper leans on

27 extracted references · 26 canonical work pages

[14]

Optimization Methods Rooting in Optimal Control

H. Zhang, and H. Wang. Optimization methods rooting in o ptimal control. arXiv preprint arXiv:2312.01334, 1-8, 2024

work page Pith review arXiv 2024
[23]

H. Wang, Y . Xu, Z. Guo, and H. Zhang. Superlinear Optimiz ation Algorithms. arXiv preprint arXiv:2403.11115, 2024

work page Pith review arXiv 2024
[22]

Y . Xu, Z. Guo, K. Lu, and H. Zhang. Distributed Optimiza- tion Algorithm with Superlinear Convergence Rate. arXiv preprint arXiv:2409.12392, 2024

work page Pith review arXiv 2024
[20]

Olfati-Saber and R

R. Olfati-Saber and R. M. Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control , vol. 49, no. 9, pp. 1520-1533, 2004. IEEE

work page 2004
[1]

Belegundu, and R

D. Belegundu, and R. Chandrupatla. Optimization concep ts and appli- cations in engineering. Journal of Management , 52(11): 56, 2000

work page 2000
[2]

Eini, and S

R. Eini, and S. Abdelwahed. Distributed model predictiv e control for intelligent traﬁc system. International Conference on Internet of Things (iThings), 909-915, 2019

work page 2019
[3]

Molzahn, F

K. Molzahn, F. D ¨orﬂer, H. Sandberg, H. Low, S. Chakrabarti, R. Baldick, and J. Lavaei. A survey of distributed optimizatio n and control algorithms for electric power systems. IEEE Transactions on Smart grid, 8(6): 2941-2962, 2017

work page 2017
[4]

Olshevsky

A. Olshevsky. Efﬁcient Information Aggregation for Dis tributed Control and Signal Processing. Ph.D. dissertation, MIT, Cambridge, MA, 2010

work page 2010

Show all 27 references

[5]

Y . Xue, B. Li, and K. Nahrstedt. Optimal resource allocat ion in wireless ad hoc networks: a price-based approach. IEEE Transactions on Mobile Computing, 5(4):347–364, 2006

2006
[6]

Wan, and D

P . Wan, and D. Lemmon. Event-triggered distributed opti mization in sensor networks. International Conference on Information Processing in Sensor Networks , 49-60, 2009

2009
[7]

Nedi ´c, and A

A. Nedi ´c, and A. Ozdaglar. Distributed subgradient methods for mult i- agent optimization. IEEE Transactions on Automatic Control , 54(1): 48–61, 2009

2009
[8]

Ozdaglar, and A

A.Nedi ´c, A. Ozdaglar, and A. Parrilo. Constrained consensus and optimization in multi-agent networks. IEEE Transactions on Automatica Control, 55(4): 922-938, 2010

2010
[9]

Islamov, X

R. Islamov, X. Qian, and P . Richt ´arik. Distributed second order methods with fast rates and compressed communication. Proceedings of the 38 th International Conference on Machine Learning , 139: 4617-4628, 2021

2021
[10]

E. Wei, A. Ozdaglar, and A. Jadbabaie. A distributed New ton method for network utility maximization-I: Algorithm. IEEE Transactions on Automatic Control, 58(9): 2162-2175, 2013

2013
[11]

E. Wei, A. Ozdaglar, and A. Jadbabaie. A distributed New ton method for network utility maximization-II: Convergence. IEEE Transactions on Automatic Control , 58(9): 2176-2188
[12]

Zhang, K

J. Zhang, K. Y ou, and T. Bas ¸ar. Distributed adaptive Ne wton methods with global superlinear convergence. Automatica,138: 110156, 2022

2022
[13]

V aragnolo, F

D. V aragnolo, F. Zanella, A. Cenedese, G. Pillonetto, a nd L. Schenato. Newton-Raphson consensus for distributed convex optimiza tion. IEEE Transactions on Automatica Control , 61(4): 994-1009, 2016

2016
[15]

V . D. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Ts itsiklis. Convergence in multiagent coordination, consensus, and ﬂo cking. Pro- ceedings of the 44th IEEE Conference on Decision and Control , pp. 2996-3000, 2005. IEEE

2005
[16]

S. Ruder. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747, 2016

2016 arXiv
[17]

Zhang, J

L. Zhang, J. Xu, H. Zhang, and L. Xie. Distributed Optima l Control and Application to Consensus of Multi-Agent Systems. arXiv preprint arXiv:2309.12577, 2023

2023 arXiv
[18]

Zhang, H

H. Zhang, H. Wang, and L. Li. Adapted and casual maximum p rinciple and analytical solution to optimal control for stochastic m ultiplica- tivenoise systems with multiple input-delays. in Proc. 51st IEEE Conf. Decision Control, Maui, HI, USA , pp. 2122–2127, 2012

2012
[19]

Qu and N

G. Qu and N. Li. Harnessing smoothness to accelerate dis tributed optimization. IEEE Transactions on Control of Network Systems , vol. 5, no. 3, pp. 1245-1260, 2017. IEEE

2017
[21]

Soori, K

S. Soori, K. Mishchenko, A. Mokhtari, M. M. Dehnavi, and M. Gur- buzbalaban. DAve-QN: A distributed averaged quasi-Newton method with local superlinear convergence rate. International Conference on Artiﬁcial Intelligence and Statistics , pp. 1965-1976, 2020. PMLR

1965
[24]

Zhang, K

J. Zhang, K. Y ou, and T. Bas ¸ar. Distributed adaptive Ne wton methods with global superlinear convergence. Automatica, vol. 138, pp. 110156,
[25]

Charalambous and C

T. Charalambous and C. N. Hadjicostis. Laplacian-base d matrix design for ﬁnite-time average consensus in digraphs. 2018 IEEE Conference on Decision and Control (CDC) , pp. 3654-3659, 2018. IEEE

2018
[26]

Boyd and L

S. Boyd and L. V andenberghe. Convex optimization. Camb ridge University Press, 2004

2004
[27]

Wang, M.X

S.G. Wang, M.X. Wu, and Z.Z. Jia. Matrix inequalities. Chinese Science Press, Beijing , 2006

2006

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [14]

Optimization Methods Rooting in Optimal Control

H. Zhang, and H. Wang. Optimization methods rooting in o ptimal control. arXiv preprint arXiv:2312.01334, 1-8, 2024

work page Pith review arXiv 2024

[2] [23]

H. Wang, Y . Xu, Z. Guo, and H. Zhang. Superlinear Optimiz ation Algorithms. arXiv preprint arXiv:2403.11115, 2024

work page Pith review arXiv 2024

[3] [22]

Y . Xu, Z. Guo, K. Lu, and H. Zhang. Distributed Optimiza- tion Algorithm with Superlinear Convergence Rate. arXiv preprint arXiv:2409.12392, 2024

work page Pith review arXiv 2024

[4] [20]

Olfati-Saber and R

R. Olfati-Saber and R. M. Murray. Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control , vol. 49, no. 9, pp. 1520-1533, 2004. IEEE

work page 2004

[5] [1]

Belegundu, and R

D. Belegundu, and R. Chandrupatla. Optimization concep ts and appli- cations in engineering. Journal of Management , 52(11): 56, 2000

work page 2000

[6] [2]

Eini, and S

R. Eini, and S. Abdelwahed. Distributed model predictiv e control for intelligent traﬁc system. International Conference on Internet of Things (iThings), 909-915, 2019

work page 2019

[7] [3]

Molzahn, F

K. Molzahn, F. D ¨orﬂer, H. Sandberg, H. Low, S. Chakrabarti, R. Baldick, and J. Lavaei. A survey of distributed optimizatio n and control algorithms for electric power systems. IEEE Transactions on Smart grid, 8(6): 2941-2962, 2017

work page 2017

[8] [4]

Olshevsky

A. Olshevsky. Efﬁcient Information Aggregation for Dis tributed Control and Signal Processing. Ph.D. dissertation, MIT, Cambridge, MA, 2010

work page 2010