Remarks on Solutions to a Nonconvex Quadratic Programming Test Problem
Bibliographic record
Abstract
A recent paper of Tuy and Hoai-Phuong published in JOGO (2007) 37:557---569 presents an algorithm for nonconvex quadratic programming with quadratic constraints. Performance of this algorithm is illustrated by solving, among others, a test problem from a paper of Audet, Hansen, Jaumard and Savard published in Mathematical Programming, Ser. A (2000) 87:131---152. This test problem is a reformulation of a problem from a paper of Dembo published in Mathematical Programming (1976) 10:192---213. Tuy and Hoai-Phuong observe that the optimal solution reported by Audet et al. is very far from the optimal one for this reformulation. The discrepancy between the reported optimal solutions is not due to selection of an almost feasible solution far from the optimal one nor to cumulation of termwise approximation errors. It is, in fact, simply due to a typographical error.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.057 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.019 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".