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AMIGO makes all-sky imaging from a lunar-orbit radio array computationally feasible by cutting memory and time costs while folding in controllable physical priors.

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AMIGO reconstructs all-sky radio maps from lunar-orbit array visibilities by combining mini-batch gradient descent with ALM priors, cutting memory and time costs enough for NSIDE=256 maps on mock DSL data.

T0 review reviewed 2026-07-14 challenge →

load-bearing objection Solid engineering paper: AMIGO makes all-sky lunar-orbit imaging computationally tractable on mocks via MBGD+ALM, with clean scaling and honest limits. the 2 major comments →

arxiv 2607.11006 v1 pith:OMH25IHT submitted 2026-07-13 astro-ph.IM

Synthesis imaging with a lunar orbit array: III. Augmented lagrangian Multiplier Imaging using Gradient descent Optimization (AMIGO)

Meng Zhou , Furen Deng , Yidong Xu , Xuelei Chen This is my paper
classification astro-ph.IM
keywords radio interferometryaperture synthesislunar orbit arrayall-sky imagingmini-batch gradient descentaugmented Lagrangianangular power spectrum prior
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

Low-frequency radio astronomy below 30 MHz is blocked from the ground by the ionosphere and Earth-based interference, so missions like the proposed DSL lunar-orbit array aim to open that window. The catch is that an orbiting array sees nearly the whole sky with constantly changing three-dimensional baselines, and classical image reconstruction becomes prohibitively expensive in memory and time. This paper introduces AMIGO, which replaces full matrix inversion with mini-batch gradient descent and wraps physical constraints (non-negative sky temperature and a prior angular power spectrum) inside an augmented Lagrangian multiplier. The result is memory that scales only with the number of sky pixels and wall-clock time that stays well below the cubic cost of traditional methods. Tests on mock DSL visibilities recover diffuse structure and bright sources from 3 to 30 MHz up to NSIDE=256, showing that high-resolution all-sky maps from lunar orbit are now within practical reach.

Core claim

AMIGO reconstructs all-sky maps from the dynamic, non-coplanar baselines of a lunar-orbit array by solving a constrained least-squares problem with mini-batch gradient descent and an augmented Lagrangian multiplier; memory falls from O(N^{2}) to O(N) and time falls from O(N^{3}+MN^{2}) to O(<MN^{2}), while adjustable residual thresholds let the user dial the strength of non-negativity and angular-power-spectrum priors.

What carries the argument

The AMIGO iteration: an outer ALM loop that updates Lagrange multipliers and penalty parameters for the equality constraint H_ℓ=0 (power-spectrum match) and inequality G_n≥0 (positive temperature), and an inner mini-batch gradient-descent step that updates sky temperatures from subsets of the visibility data without ever forming the full response matrix.

Load-bearing premise

That idealized mock visibilities—perfect orbits, opaque Moon, ideal beams, and pure thermal noise with no calibration or baseline errors—are realistic enough to prove the method will work on actual flight data.

What would settle it

Run AMIGO on the same mock data after injecting realistic baseline-determination phase errors or primary-beam model mismatches; if the residual maps and MSE degrade beyond the levels reported for pure thermal noise, the claim of practical feasibility fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper introduces AMIGO, an imaging algorithm for lunar-orbiting interferometers such as DSL that combines Mini-Batch Gradient Descent with the Augmented Lagrangian Multiplier method. It formulates all-sky reconstruction as a constrained optimization problem (data fidelity plus non-negative temperature and angular-power-spectrum equality constraints), converts it via ALM into an unconstrained problem whose first sub-step is solved by MBGD, and controls prior strength through residual thresholds ΔH and ΔG. Mock visibilities generated under a realistic DSL orbit (breathing baselines, lunar shading, short-dipole beams) are used to reconstruct maps at 3, 10 and 30 MHz up to NSIDE = 256. The authors report MSE/SSIM/ρℓ metrics, demonstrate hierarchical initialization, and show that memory and wall-clock scaling improve relative to the Tikhonov-regularization matrix-inversion approach of Deng et al. (2026).

Significance. If the claimed scalings hold under more realistic systematics, AMIGO would remove a genuine computational bottleneck for all-sky imaging with dynamic 3-D baselines, making NSIDE ≥ 256 reconstructions feasible on modest hardware. The ALM residual-threshold mechanism supplies a transparent, adjustable way to inject physically motivated priors (non-negativity and Cℓ) without hard-wiring a full prior map. The hierarchical-initialization strategy and the explicit GPU/CPU benchmarks against D26 are concrete engineering contributions that other lunar-array concepts can reuse. The work is therefore a useful algorithmic step for the DSL and similar missions, even though it remains a proof-of-concept on idealized mocks.

major comments (2)
  1. §6 and §3 explicitly limit validation to mocks that omit calibration errors, baseline uncertainties and beam-model errors (opaque Moon, perfect antennas pointed at lunar center, white Gaussian noise only). The central feasibility claim for real DSL data therefore rests on an untested extrapolation. A quantitative stress test—e.g., injecting the phase errors already characterized in Zhou et al. (2026) and re-measuring MSE/SSIM/ρℓ—is needed before the claim can be regarded as demonstrated rather than projected.
  2. §5.1 and Table 2: when the prior Cℓ is scaled by 1.5 the reconstruction develops artificial stripes and MSE rises from 0.053 to 0.303. The only diagnostic offered is “unacceptable iteration count.” Because a true Cℓ will never be known a priori, the paper should supply a practical, data-driven procedure (or at least a quantitative criterion) for detecting and correcting such mismatches without access to the input map.
minor comments (5)
  1. Table 3 / Figure 7: wall-clock times are hardware-specific (RTX 3090 + EPYC 9654). State the software stack (CUDA version, BLAS library) and report FLOPs or iteration-normalized timings so that the O(Nvis Npix) scaling can be verified independently.
  2. Equation (9) and surrounding text: the learning-rate schedule (initial α = 1.0, decay 0.1, increase 1.2, floor 10−7) is described but never ablated. A short sensitivity check would strengthen the claim that imaging quality is insensitive to batch configuration.
  3. Figures 1–3: color-bar ranges differ between frequencies; a common fractional-residual scale or an additional panel of absolute residuals would aid visual comparison.
  4. Appendix A: the factor of 2 that appears after the spherical-harmonic chain rule is correct for real maps, but a one-sentence reminder that aℓ,−m = (−1)m a*ℓm would help readers less familiar with HEALPix conventions.
  5. Typographical: “Augmented lagrangian” should be consistently capitalized; “breathing” strategy is introduced without a citation to the earlier DSL papers that define it.

Circularity Check

1 steps flagged

No load-bearing circularity: AMIGO is a standard ALM+MBGD application whose claims are validated on independent mocks and measured against a prior method; only minor series self-citation for setup/comparison.

specific steps
  1. self citation load bearing [§1, §5.4–5.5, citations to D26 / Shi et al. 2022 / Huang et al. 2018]
    "To enhance algorithm performance under practical issues, F. Deng et al. (2026) (hereinafter D26) incorporated a “breathing” strategy … We also compare AMIGO with previous approaches. … Comparisons with the TR approach in D26 quantitatively verify the computation gain of AMIGO"

    The orbit configuration, visibility model, and Tikhonov baseline are taken from the authors’ own prior papers in the same series. This is ordinary cumulative work, not a uniqueness theorem or definitional reduction that forces the AMIGO results; the new algorithm, its gradients, residual control, and measured wall-clock/memory numbers stand independently. Flagged only as minor non-load-bearing self-citation.

full rationale

The paper formulates a constrained least-squares imaging problem (Eqs. 1–5), converts it via ALM (Eqs. 6–8) with explicit residual thresholds controlling prior strength, and solves the differentiable subproblem by mini-batch gradient descent with derived gradients (Appendix A). These steps are textbook optimization applied to the known interferometric forward model; nothing is defined in terms of the reconstructed map or fitted to force a later “prediction.” Validation uses mock visibilities generated from known input skies under stated orbit/beam/noise assumptions (§3); reconstruction quality (MSE, SSIM, ρ_ℓ) is measured against those inputs and against the Tikhonov method of D26 on identical data (§5.4–5.5, Tables 2–4, Figs. 7–8). When the C_ℓ prior is deliberately mismatched (§5.1, Fig. 5), quality degrades and iteration counts rise, confirming the prior is not circularly forced. Self-citations to the DSL series (Huang 2018, Shi 2022, D26) supply the mission configuration and a baseline comparator; they are not uniqueness theorems or load-bearing premises that make the computational-scaling or reconstruction claims true by construction. The claimed O(N) memory / <O(MN^{2}) time scalings are independently measured (Table 3, Fig. 7). The only residual softness is the mock-only validation already flagged by the authors (§6), which is a scope limitation, not circularity. Score 1 reflects ordinary series self-citation that is not load-bearing.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard optimization theory, domain models of lunar-orbit interferometry taken from the authors’ earlier papers, and a handful of tunable numerical thresholds chosen for the mock experiments. No new physical entities are postulated; the free parameters are algorithmic knobs whose values are reported and whose impact is explored.

free parameters (5)
  • Δ_thres_H (angular-power-spectrum residual threshold) = 0.01 / 0.03
    Controls prior strength; fiducial values 0.01 (3 & 10 MHz) or 0.03 (30 MHz) chosen by hand and varied in §5.1.
  • Δ_thres_G (non-negativity residual threshold) = 0.01
    Fixed at 0.01 for all runs; controls how strictly sky temperature ≥ 0 is enforced.
  • N_mini (mini-batch size) = 2^18
    Set to 2^18 in fiducial runs; varied over 2^16–2^20 with little effect (§5.2).
  • learning-rate schedule (α init=1.0, decay 0.1, increase 1.2) = init 1.0
    Backtracking-like rule with hard floor 10^{-7}; chosen for stable convergence on the quadratic cost.
  • ρ1, ρ2 (ALM penalty factors)
    Increased adaptively until residual thresholds are met; must reach ≥100× initial values.
axioms (5)
  • domain assumption Visibility is a linear integral of sky temperature times beam, shading and fringe phase (Eq. 10).
    Standard radio-interferometry measurement equation; adopted unchanged from Huang+2018, Shi+2022, Deng+2026.
  • domain assumption Moon is a fully opaque sphere that neither radiates, diffracts nor reflects (§3.1).
    Simplifies the shading function; stated explicitly as a modeling choice.
  • domain assumption Thermal noise is white Gaussian with variance given by the radiometer equation (Eq. 13).
    Standard assumption for uncorrelated receiver noise; used to generate mocks.
  • standard math ALM converts the constrained problem into an unconstrained one whose stationary points satisfy the original constraints when ρ→∞ (Eqs. 6–7).
    Classic result of Hestenes/Powell/Rockafellar; invoked without re-proof.
  • ad hoc to paper Hierarchical upgrade of lower-NSIDE solutions supplies good initial guesses that avoid many local minima (§4, §5.3).
    Empirical strategy validated only on the mocks; not derived from first principles.

reviewed 2026-07-14 · how reviews work

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Cite this review

Pith. "Pith review of Synthesis imaging with a lunar orbit array: III. Augmented lagrangian Multiplier Imaging using Gradient descent Optimization (AMIGO)." pith.science (2026). https://pith.science/paper/OMH25IHT

@misc{pith2026260711006,
  author       = {Pith},
  title        = {Pith review of: Synthesis imaging with a lunar orbit array: III. Augmented lagrangian Multiplier Imaging using Gradient descent Optimization (AMIGO)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OMH25IHT}},
  note         = {Machine review of arXiv:2607.11006}
}
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read the original abstract

Ground-based radio observations below 30 MHz are severely limited by ionospheric interference and radio frequency interference (RFI) from Earth. A lunar-orbiting radio interferometer mission, the Discovering the Sky at the Longest wavelength (DSL, also known by its Chinese name ``Hongmeng''), has been proposed to overcome these obstacles. However, for such a mission, there are new challenges, such as the nearly all-sky field of view and dynamic 3D baselines, which require a huge computational cost for interferometric image reconstruction. In this work, we present AMIGO (Augmented lagrangian Multiplier Imaging using Gradient descent Optimization), a novel imaging algorithm tailored to lunar-orbiting arrays like DSL, combining the Mini-Batch Gradient Descent (MBGD) method with the Augmented Lagrangian Multiplier (ALM) technique. MBGD reduces the computational complexity and memory cost, enabling efficient handling of large datasets. ALM flexibly incorporates physical priors like non-negative sky temperature and prior angular power spectrum into the imaging algorithm, with adjustable stopping criteria to quantitatively control prior strength. We validate AMIGO using mock visibility data generated under realistic DSL orbit configurations. Reconstructed sky maps at various frequencies and spatial resolutions show that this approach provides a computationally feasible framework for all-sky imaging with a lunar-orbiting array.

Figures

Figures reproduced from arXiv: 2607.11006 by Furen Deng, Meng Zhou, Xuelei Chen, Yidong Xu.

Figure 1
Figure 1. Figure 1: Reconstructed maps at 3.0 MHz with NSIDE = 64. We plot the reconstructed sky maps without (Left) and with (Right) thermal noise in the middle panels, and the fractional residuals in the bottom panels. We also plot the input map downgraded to NSIDE = 64 in the top panel for comparison [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: ρℓ over various prior settings and batch configurations. We vary the strength of the prior in the left panel, the mini-batch size in the middle, and the ordering in the right. We find that ρℓ drops at ℓ ∼ 3 with ∆thre H = 0.05. We do not find significant differences among the batch configurations tested in this work [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The reconstructed maps at 3.0 MHz with NSIDE = 64, using different C prior ℓ . We use 1 × C inp ℓ as the prior in the left panel, 1.05 × C inp ℓ in the middle, and 1.50 × C inp ℓ in the right. The reconstructed map in the large error case appears much brighter and displays artificial stripes. One may obtain better imaging quality using visibility data in a certain order because they anticipate image recons… view at source ↗
Figure 6
Figure 6. Figure 6: Convergence verification of AMIGO with respect to the initial guesses and the noise realizations. We plot the MSE of reconstructed maps at 3.0 MHz (Left) and 10.0 MHz (Middle) as a function of the ratio (s 0 /s¯ true). Unbiased flat initial guesses consistently yield good reconstructions. The hierarchical setting can alleviate dependence on biased initial guesses. In the right panel, we plot the MSE for va… view at source ↗
Figure 7
Figure 7. Figure 7: Computational costs of D26 and AMIGO normal￾ized with the minimum case as a function of NSIDE. We also plot the fitted scaling with expected templates in dashed lines. We find that both in time and space, AMIGO costs much less and scales much better. which can be considered as a pixel-averaging strategy at the level of the reconstructed map. We also verify that AMIGO cannot work beyond the Nyquist limit in… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of ρℓ between D26 and AMIGO. We plot ρℓ at 3.0 MHz in the top panel and 10.0 MHz in the bot￾tom, respectively. We find that with a correct prior map, TR is better than AMIGO at 10.0 MHz but does not have signif￾icant improvements at 3.0 MHz. The fractional differences between the reconstructed maps at 3.0 MHz with and with￾out the prior correction are around 10−5 , unnoticeably small in the ρℓ p… view at source ↗
Figure 9
Figure 9. Figure 9: The reconstructed maps at 3.0 MHz with NSIDE = 64, using visibility data of different baseline ranges. We use visibility data of baselines b < bNQ in the left panel, b < 2bNQ in the middle, and b < 4bNQ in the right. We find strong aliasing effects if the skymaps are reconstructed using visibility data beyond the Nyquist limit. REFERENCES Abadi, M., Agarwal, A., Barham, P., et al. 2015,, https://www.tensor… view at source ↗

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Reference graph

Works this paper leans on

35 extracted references · 17 canonical work pages

  1. [1]

    2015,, https://www.tensorflow.org/ Google

    Abadi, M., Agarwal, A., Barham, P., et al. 2015,, https://www.tensorflow.org/ Google

    2015

  2. [2]

    V., Bioucas-Dias, J

    Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. 2010, IEEE Transactions on Image Processing, 19, 2345, doi: 10.1109/TIP.2010.2047910

    work page doi:10.1109/tip.2010.2047910 2010

  3. [3]

    V., Bioucas-Dias, J

    Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. 2011, IEEE Transactions on Image Processing, 20, 681, doi: 10.1109/TIP.2010.2076294

    work page doi:10.1109/tip.2010.2076294 2011

  4. [4]

    2025, ApJ, 994, 226, doi: 10.3847/1538-4357/ae19e9

    Ao, Q., Deng, F., Xu, Y., et al. 2025, ApJ, 994, 226, doi: 10.3847/1538-4357/ae19e9

    work page doi:10.3847/1538-4357/ae19e9 2025

  5. [5]

    2024, RAS Techniques and Instruments, 4, rzae061, doi: 10.1093/rasti/rzae061

    Artuc, K., & de Lera Acedo, E. 2024, RAS Techniques and Instruments, 4, rzae061, doi: 10.1093/rasti/rzae061

    doi:10.1093/rasti/rzae061 2024

  6. [6]

    Bale, S. D. 2023, in AGU Fall Meeting Abstracts, Vol. 2023, P31B–02

    2023

  7. [7]

    2021, in 2021 IEEE Aerospace Conference (50100), 1–25, doi: 10.1109/AERO50100.2021.9438165

    Bandyopadhyay, S., Mcgarey, P., Goel, A., et al. 2021, in 2021 IEEE Aerospace Conference (50100), 1–25, doi: 10.1109/AERO50100.2021.9438165

    doi:10.1109/aero50100.2021.9438165 2021

  8. [8]

    N., & Gharpure, D

    Borade, R., George, G. N., & Gharpure, D. C. 2021, in American Institute of Physics Conference Series, Vol. 2335, American Institute of Physics Conference Series (AIP), 030005, doi: 10.1063/5.0043435

    work page doi:10.1063/5.0043435 2021

  9. [9]

    Burns, J. O. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20190564, doi: 10.1098/rsta.2019.0564

    doi:10.1098/rsta.2019.0564 2021

  10. [10]

    O., Bale, S., & Bradley, R

    Burns, J. O., Bale, S., & Bradley, R. F. 2019, in American Astronomical Society Meeting Abstracts, Vol. 234, American Astronomical Society Meeting Abstracts #234, 212.02

    2019

  11. [11]

    O., Bradley, R., Tauscher, K., et al

    Burns, J. O., Bradley, R., Tauscher, K., et al. 2017, ApJ, 844, 33, doi: 10.3847/1538-4357/aa77f4

    work page doi:10.3847/1538-4357/aa77f4 2017

  12. [12]

    2010, Multiscale Modeling & Simulation, 8, 337, doi: 10.1137/090753504

    Cai, J.-F., Osher, S., & Shen, Z. 2010, Multiscale Modeling & Simulation, 8, 337, doi: 10.1137/090753504

    work page doi:10.1137/090753504 2010

  13. [13]

    M., Slosar, A., et al

    Camacho, H., Rotermund, K. M., Slosar, A., et al. 2025, arXiv e-prints, arXiv:2508.16773, doi: 10.48550/arXiv.2508.16773

    work page doi:10.48550/arxiv.2508.16773 2025

  14. [14]

    2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20190566, doi: 10.1098/rsta.2019.0566

    Chen, X., Yan, J., Deng, L., et al. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20190566, doi: 10.1098/rsta.2019.0566

    doi:10.1098/rsta.2019.0566 2021

  15. [15]

    2023, Chinese Journal of Space Science, 43, 43

    Chen, X., Yan, J., Xu, Y., et al. 2023, Chinese Journal of Space Science, 43, 43

    2023

  16. [16]

    2024, arXiv e-prints, arXiv:2403.16409, doi: 10.48550/arXiv.2403.16409

    Chen, X., Gao, F., Wu, F., et al. 2024, arXiv e-prints, arXiv:2403.16409, doi: 10.48550/arXiv.2403.16409

    Pith/arXiv arXiv doi:10.48550/arxiv.2403.16409 2024

  17. [17]

    N., & V¨ omel, C

    Demmel, J., Marques, O., Parlett, B. N., & V¨ omel, C. 2007, SIAM Journal on Scientific Computing, 29, 1365, doi: 10.1137/06065029X

    work page doi:10.1137/06065029x 2007

  18. [18]

    2026, AJ, 171, 100, doi: 10.3847/1538-3881/ae2d21

    Deng, F., Xu, Y., Wu, F., et al. 2026, AJ, 171, 100, doi: 10.3847/1538-3881/ae2d21

    work page doi:10.3847/1538-3881/ae2d21 2026

  19. [19]

    Eckstein, J., & Bertsekas, D. P. 1992, Mathematical programming, 55, 293

    1992

  20. [20]

    2009, SIAM Journal on Imaging Sciences, 2, 323, doi: 10.1137/080725891

    Goldstein, T., & Osher, S. 2009, SIAM Journal on Imaging Sciences, 2, 323, doi: 10.1137/080725891

    doi:10.1137/080725891 2009

  21. [21]

    Hestenes, M. R. 1969, Journal of optimization theory and applications, 4, 303

    1969

  22. [22]

    J., Burns, J

    Hibbard, J. J., Burns, J. O., MacDowall, R., et al. 2026, AJ, 171, 26, doi: 10.3847/1538-3881/ae18d8

    doi:10.3847/1538-3881/ae18d8 2026

  23. [23]

    2018, AJ, 156, 43, doi: 10.3847/1538-3881/aac6c6 18

    Huang, Q., Sun, S., Zuo, S., et al. 2018, AJ, 156, 43, doi: 10.3847/1538-3881/aac6c6 18

    work page doi:10.3847/1538-3881/aac6c6 2018

  24. [24]

    R., & Johansson, M

    Khirirat, S., Feyzmahdavian, H. R., & Johansson, M. 2017, in 2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2880–2887, doi: 10.1109/CDC.2017.8264077 Klein Wolt, M., Falcke, H., & Koopmans, L. 2024, in American Astronomical Society Meeting Abstracts, Vol. 243, American Astronomical Society Meeting Abstracts, 264.01

    work page doi:10.1109/cdc.2017.8264077 2017

  25. [25]

    2025, arXiv e-prints, arXiv:2507.13102, doi: 10.48550/arXiv.2507.13102 Mart´ ınez, H., Catal´ an, S., Igual, F

    Li, H., Deng, F., Zhou, M., Xu, Y., & Chen, X. 2025, arXiv e-prints, arXiv:2507.13102, doi: 10.48550/arXiv.2507.13102 Mart´ ınez, H., Catal´ an, S., Igual, F. D., Herrero, J. R., & Quintana-Ort´ ı, E. S. 2025, Cluster Computing, 28, 779, doi: 10.1007/s10582-025-02456-1

    work page doi:10.48550/arxiv.2507.13102 2025

  26. [26]

    2018, arXiv e-prints, arXiv:1804.07612, doi: 10.48550/arXiv.1804.07612

    Masters, D., & Luschi, C. 2018, arXiv e-prints, arXiv:1804.07612, doi: 10.48550/arXiv.1804.07612

    Pith/arXiv arXiv doi:10.48550/arxiv.1804.07612 2018

  27. [27]

    Nocedal, J., & Wright, S. J. 2006, Numerical Optimization, 2nd edn. (Springer)

    2006

  28. [28]

    2019, in Advances in Neural Information Processing Systems, 8024–8035

    Paszke, A., Gross, S., Massa, F., et al. 2019, in Advances in Neural Information Processing Systems, 8024–8035

    2019

  29. [29]

    S., Burns, J

    Polidan, R. S., Burns, J. O., Ignatiev, A., et al. 2024, Advances in Space Research, 74, 528, doi: 10.1016/j.asr.2024.04.008

    work page doi:10.1016/j.asr.2024.04.008 2024

  30. [30]

    Powell, M. J. D. 1969, in Proceedings of the 1969 IFIP Congress (Amsterdam: North-Holland), 283–298

    1969

  31. [31]

    Rockafellar, R. T. 1974, SIAM Journal on Control, 12, 268, doi: 10.1137/0312021 Sathyanarayana Rao, M., Singh, S., K. S., S., et al. 2023, Experimental Astronomy, 56, 741, doi: 10.1007/s10686-023-09909-5

    doi:10.1137/0312021 1974

  32. [32]

    2022, MNRAS, 510, 3046, doi: 10.1093/mnras/stab3623

    Shi, Y., Xu, Y., Deng, L., et al. 2022, MNRAS, 510, 3046, doi: 10.1093/mnras/stab3623

    work page doi:10.1093/mnras/stab3623 2022

  33. [33]

    2023, Research in Astronomy and Astrophysics, 23, 125017, doi: 10.1088/1674-4527/ad019d

    Yang, X., Wang, M., Wu, L., et al. 2023, Research in Astronomy and Astrophysics, 23, 125017, doi: 10.1088/1674-4527/ad019d

    work page doi:10.1088/1674-4527/ad019d 2023

  34. [34]

    2026, AJ, 171, 298, doi: 10.3847/1538-3881/ae5935

    Zhou, M., Deng, F., Xu, Y., Zhou, L., & Chen, X. 2026, AJ, 171, 298, doi: 10.3847/1538-3881/ae5935

    work page doi:10.3847/1538-3881/ae5935 2026

  35. [35]

    Zhu, J., Acedo, E. d. L., Artuc, K., & Chen, X. 2025, RAS Techniques and Instruments, 4, rzae064, doi: 10.1093/rasti/rzae064

    work page doi:10.1093/rasti/rzae064 2025

This paper was first reviewed by grok-4.5 on July 14, 2026.