Mathematical claims
A kidney-exchange model allows one patient to receive two kidneys
KidneyExchange.jl: a Julia package for solving the kidney exchange problem with branch-and-price · Mathematical Programming Computation, 2024
What happened
Two altruist chains can end at the same patient in the printed model. The relevant constraint counts outgoing chain arcs, so a patient at the end of a chain appears unused even when two selected chains both send a kidney to that patient.
Why it matters
The printed formulation admits an impossible transplant plan. The appendix and released code use incoming arcs instead, so this finding does not invalidate the paper’s reported computation table.
Algorithms and code
An exact method returns 3 when the true optimum is 2
Exact methods for discrete Γ-robust interdiction problems with an application to the bilevel knapsack problem · Mathematical Programming Computation, 2023
What happened
The implementation passes profits and weights to a helper in the wrong order. On a two-item example, it treats a selection with true weight 11 as having weight 3 under a capacity of 10, then reports objective 3 with zero optimality gap.
Why it matters
The code can certify a suboptimal answer as exact. A bounded rerun reached the faulty path in 189 of 560 tested parameter combinations, but that does not mean 189 published results are wrong.
Agreement between paper and code
The paper uses the ℓ₂ norm while the code uses ℓ₁
A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians · Mathematics of Operations Research, 2024
What happened
The convergence analysis defines its model with the Euclidean norm, but the implementation evaluates the one-norm. For one residual vector, the paper predicts a positive reduction of 0.151, while the code computes −0.2.
Why it matters
The sign reversal can change merit-parameter updates, step acceptance, and later iterates. The proof therefore does not cover the released computation.
Files needed to reproduce results
The released results omit one complete comparison method
Relaxations for Binary Polynomial Optimization via Signed Certificates · Mathematics of Operations Research, 2026
What happened
The public archive contains 240 result files, but all 48 expected records for one comparison method are missing. The supplied aggregation program starts the comparison and then stops when it reaches the absent data.
Why it matters
A table and figure cannot be regenerated from the released files. Missing inputs establish a reproduction failure; they do not show that the published values themselves are false.
Numerical error and tolerances
A tolerance creates a 1.67-million-fold derivative error
Conic Optimization with Spectral Functions on Euclidean Jordan Algebras · Mathematics of Operations Research, 2023
What happened
The spectral code uses an absolute tolerance to decide that two distinct eigenvalues are equal. It then substitutes the repeated-eigenvalue formula, returning 5.56 × 10³⁰ instead of the correct 3.33 × 10²⁴.
Why it matters
Hessian and higher-derivative calculations can be corrupted in ill-conditioned cases. The symbolic formula is unaffected, and the audit did not establish that a published table contains this particular case.
Reported results and metrics
An optimality checker accepts a worse point—and NaN values
OSQP: an operator splitting solver for quadratic programs · Mathematical Programming Computation, 2020
What happened
For a one-variable problem whose unique solution is x = 1 with objective −0.5, the benchmark checker accepts x = 0 with objective 0. It also accepts vectors containing only NaN values because its comparisons never flag them.
Why it matters
A benchmark result can be marked optimal without a valid certificate. This finding concerns the checker, not the core OSQP solver, and historical solution vectors were unavailable for testing published rows.
Time, memory, and compute
The released timings do not support the claimed 2.5-fold speedup
A derivative-free Gauss–Newton method · Mathematical Programming Computation, 2019
What happened
At the endpoint cited in the paper, the deposited wall-clock data show a 1.32-fold speedup. The deposited CPU times instead make the focal method 2.12 times slower per iteration.
Why it matters
Neither recorded clock supports the 2.5-fold claim. The paper’s separate memory comparison and asymptotic storage argument are unaffected.
Experiment design and uncertainty
The confidence intervals are too wide by √2
Unichain and Aperiodicity Are Sufficient for Asymptotic Optimality of Average-Reward Restless Bandits · Mathematics of Operations Research, 2025
What happened
The stated estimator uses 20 batch means, but the plotting code divides by √10 rather than √20. This makes every displayed interval about 41% wider than the formula in the manuscript.
Why it matters
The point estimates are unchanged and the error is conservative, but the uncertainty display does not implement the estimator the paper describes.
Baselines and test coverage
A matrix-completion experiment never tests the missing entries
Low-Rank Optimization Methods Based on Projected Projected-Gradient Descent That Accumulate at Bouligand Stationary Points · Mathematics of Operations Research, 2026
What happened
The experiment fits a matrix using sampled entries and evaluates performance on those same entries. It reports no error on the unobserved entries that matrix completion is intended to recover.
Why it matters
The experiment measures how quickly the method fits observed data, not whether it accurately reconstructs missing data. A held-out or full-matrix error is needed for the recovery claim.
Citations and prior work
A claimed first manifold ADMM has an earlier predecessor
A Riemannian Alternating Direction Method of Multipliers · Mathematics of Operations Research, 2025
What happened
The paper claims the first ADMM-type method for a nonsmooth objective over a manifold. A public 2015 preprint, published in 2016, already presents a generic manifold ADMM for the same split problem family.
Why it matters
The broad priority claim is false. The newer paper still contributes a different update and a convergence analysis that the predecessor does not provide.
Reporting and claim scope
“Consistently outperforms” overstates the tables
A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians · Mathematics of Operations Research, 2024
What happened
One table shows 17 wins and 5 losses; another shows 19 cases won on both reported metrics and 3 exceptions. The conclusion nevertheless says the method consistently outperforms its comparator.
Why it matters
The tables support a strong majority advantage, not a universal statement. The conclusion should report the wins and exceptions directly.