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REVIEW 3 major objections 1 minor 1 cited by

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints

T0 review · 3 major / 1 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper proposes ASPEN, a quadratic-penalty algorithm with additional sampling that achieves almost sure convergence on non-convex nonlinear equality-constrained finite-sum problems.

desk verdict The abstract and the full text are different papers: the ASPEN optimization content is entirely absent, so the submission as-is is unverifiable and should not go to referees. read the letter →

arxiv 2508.02299 v1 pith:NBIFPDMV submitted 2025-08-04 math.OC cs.NAmath.NA

Nataša Krejić , Nataša Krklec Jerinkić , Tijana Ostojić , Nemanja Vučićević This is my paper
classification math.OCcs.NAmath.NA MSC 90C3090C2690C15
keywords finite-sumoptimizationnonlinearequalityconstraintsquadraticpenaltymethodadditionalsamplingalmostsureconvergencenon-convexmini-batchadaptiveparameter
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

ASPEN is an algorithm for non-convex finite-sum optimization problems with nonlinear equality constraints. It combines a quadratic penalty framework with an additional sampling strategy that adaptively adjusts the sample size used in each gradient computation, ranging from mini-batch to full sample. The method uses a non-monotone line search for step sizes and an adaptive penalty parameter, and it avoids costly projections. The central claim is that ASPEN converges almost surely to a stationary point under a standard set of assumptions, while offering computational savings through sample size adaptation. If true, this provides a practical and theoretically supported approach for large-scale equality-constrained machine learning problems.

What carries the argument

The central mechanism is the additional sampling strategy, a rule that adaptively grows the sample size used to estimate the finite-sum gradient within a quadratic penalty framework. The penalty term enforces nonlinear equality constraints, the non-monotone line search determines step sizes, and the adaptive penalty parameter balances constraint satisfaction against objective minimization. The sample size control is what carries the computational savings: early iterations use small samples and later iterations approach the full sample, which together with the penalty mechanism yields the almost sure convergence result.

What would settle it

Run ASPEN on a small non-convex problem with one nonlinear equality constraint, for example minimize f(x) = (x_1 - 1)^2 + (x_2 + 1)^2 subject to $x_1^{2}$ + $x_2^{2}$ = 1, while keeping the sample size fixed at a mini-batch that never reaches the full sample. If the iterates fail to converge to any stationary point, the claimed almost sure guarantee is refuted for this setting.

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Extended reading notes

Core claim

ASPEN establishes almost sure convergence for a quadratic penalty method that incorporates an additional sampling strategy for updating the sample size in finite-sum problems with nonlinear equality constraints. The method interpolates between mini-batch and full-sample regimes depending on the problem, uses a non-monotone line search, and adapts the penalty parameter during iterations. Its key advantage is avoiding projections onto the constraint set, which can be expensive, while maintaining a convergence guarantee. The paper demonstrates effectiveness on both academic and real-data machine learning problems.

Load-bearing premise

The almost sure convergence guarantee rests on the existence of a standard set of assumptions, including Lipschitz smoothness of the objective and boundedness of the iterates, together with an unspecified sample size update rule that must keep the sampling noise appropriately controlled.

Editorial extensions

If this is right

  • If ASPEN converges as claimed, it offers a projection-free solver for finite-sum problems with nonlinear equality constraints, reducing per-iteration cost in large-scale settings.
  • The sample size spectrum from mini-batch to full sample means users can trade off per-iteration cost against convergence behavior by controlling how quickly the sample grows.
  • The method extends the reach of additional sampling techniques from unconstrained and linearly constrained problems to the more general nonlinear equality-constrained case.
  • The non-monotone line search and adaptive penalty parameter may make the algorithm robust to poor initializations and mitigate the need for careful hyperparameter tuning.

Reading between the lines

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

  • One could test the algorithm's behavior when the sample size is artificially capped below the full sample, to see whether convergence degrades; if it does, the reported savings may not materialize for problems where reaching the full sample is essential.
  • The additional sampling rule might be adapted to other penalty-based or augmented Lagrangian methods, potentially offering similar computational benefits for inequality constraints.
  • An experimental extension could compare ASPEN against stochastic augmented Lagrangian methods on problems with many constraints to see if the projection-free property translates into wall-clock gains.
  • The convergence proof likely requires the sample size to grow at a certain rate; a practitioner could derive a concrete schedule from the proof and verify it empirically on a set of benchmark problems.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 1 minor

Summary. The submission, identified as arXiv:2508.02299 (math.OC), claims to propose an algorithm called ASPEN for non-convex, nonlinear equality-constrained finite-sum optimization problems. The abstract states that ASPEN uses an additional sampling strategy within a quadratic penalty framework, employs a non-monotone line search and an adaptive penalty parameter, avoids costly projections, and provably converges almost surely under a standard set of assumptions, with numerical experiments demonstrating effectiveness. However, the full text supplied with the submission is an entirely different paper: 'Pre-Tactical Flight-Delay and Turnaround Forecasting with Synthetic Aviation Data' by Abdulmajid Murad and Massimiliano Ruocco. This aviation paper contains no mention of ASPEN, no optimization algorithm, no convergence theorem, no list of assumptions, no proof, and no experiments on finite-sum optimization. The submitted material therefore does not contain the paper described in the abstract, and the central claims of the submission cannot be verified from the provided text.

Significance. If the ASPEN algorithm and its almost sure convergence result are correct, the work could be a useful contribution to finite-sum optimization with nonlinear equality constraints, particularly because it promises to avoid projections and to interpolate between mini-batch and full-sample regimes. However, none of that content is present in the submitted manuscript. The supplied full text is an empirical aviation-forecasting study, which does not address the mathematical claims at all. There are no machine-checked proofs, no reproducible optimization code, and no derivations in the material under review. Consequently, the significance of the claimed contribution cannot be assessed: the manuscript as submitted provides no evidence for its own central assertions.

major comments (3)
  1. [Abstract vs. Full Text] The abstract describes an algorithm called ASPEN for non-convex nonlinear equality-constrained finite-sum problems and states that 'the almost sure convergence is proved under a standard set of assumptions.' The full text, however, contains no ASPEN algorithm, no assumptions, no theorem, and no proof. Instead, the body is a paper on synthetic aviation data for flight-delay and turnaround forecasting, with different authors and a different title. The central mathematical claim of the submission is therefore entirely unsupported by the submitted material.
  2. [Full Text (all)] The abstract also claims that 'numerical experiments on both academic and real-data based machine learning problems demonstrate the effectiveness of the proposed approach.' The submitted full text reports experiments on four synthetic data generators and three aviation prediction tasks, reporting metrics such as R², RMSE, MAE, utility scores, and feature-importance alignment. None of these experiments concerns ASPEN, finite-sum optimization, quadratic penalty methods, or nonlinear equality constraints. The claimed computational savings and effectiveness of ASPEN are thus unverifiable.
  3. [Abstract (assumptions and scope)] The abstract invokes 'a standard set of assumptions' and an 'additional sampling strategy' without specifying either, and it asserts that the method is a transition of additional sampling from unconstrained and linearly constrained problems to nonlinear constraints. This extension is load-bearing for the claimed convergence result. Because the manuscript body contains no statement of assumptions and no derivation for the nonlinear-constraint case, the validity of the almost sure convergence claim cannot be checked from the submission as it stands.
minor comments (1)
  1. [Manuscript metadata] The title, author list, and subject matter of the full text do not match the abstract or the arXiv identifier's subject classification (math.OC). This mismatch should be resolved by the authors before the paper is considered further.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation exists in the submitted material; the ASPEN abstract and the full text are unrelated documents.

full rationale

The submission under the header arXiv:2508.02299 (math.OC) claims an ASPEN algorithm with an almost-sure convergence proof, but the supplied full text is an unrelated aviation paper (Murad & Ruocco, "Pre-Tactical Flight-Delay and Turnaround Forecasting with Synthetic Aviation Data") with different authors, title, and subject matter. There is no ASPEN algorithm statement, no list of assumptions, no convergence theorem, no proof, no sample-size update rule, and no optimization experiment in the full text. The claimed derivation chain is therefore absent rather than circular: no equation can be exhibited in which an output reduces by construction to an input, and no load-bearing self-citation chain can be identified. The aviation paper itself uses an empirical TSTR evaluation and does not derive its headline utility scores from fitted inputs by definition. Accordingly, per the hard rule that circularity requires quoting a specific reduction, the honest finding is no circularity (score 0). The abstract's unsupported claim that convergence is proved is flagged as missing support / omitted proof, but that is a document-integrity and verifiability failure, not a circularity.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Only the abstract is usable; the full text is unrelated. No free parameters or invented entities are visible, but the convergence claim rests on unstated standard assumptions and on the unspecified additional sampling update rule.

assumptions (1)
  • domain assumption Standard assumptions for the convergence proof hold (e.g., Lipschitz continuity of the objective gradient, boundedness of iterates, and a suitable sample size update rule).
    Invoked by the abstract's phrase 'under a standard set of assumptions'; the assumptions are not enumerated and the proof is not included.

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Cite this review

Pith. "Pith review of ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints." pith.science (2026). https://pith.science/paper/NBIFPDMV

@misc{pith2026250802299,
  author       = {Pith},
  title        = {Pith review of: ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NBIFPDMV}},
  note         = {Machine review of arXiv:2508.02299}
}
read the original abstract

We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one end, to increasing sample size that achieves the full sample eventually, on the other end of the spectrum. A non-monotone line search is used for the step size update, while the penalty parameter is also adaptive. The proposed algorithm avoids costly projections, which, together with the sample size update, may yield significant computational cost savings. Also, the proposed method can be viewed as a transition of an additional sampling approach for unconstrained and linear constrained problems, to a more general class with non-linear constraints. The almost sure convergence is proved under a standard set of assumptions for this framework, while numerical experiments on both academic and real-data based machine learning problems demonstrate the effectiveness of the proposed approach.

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Forward citations

Cited by 1 Pith paper

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  1. A Projected Stochastic Gradient Method for Finite-Sum Problems with Linear Equality Constraints

    math.OC 2026-03 unverdicted novelty 5.0 of 10

    A projected stochastic gradient method is developed for finite-sum problems with linear equality constraints, providing convergence analysis under standard assumptions and numerical results.

Reference graph

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Reviewed August 6, 2026 · model on record in the stance chip above.