A dynamic large-update primal‐dual interior-point method for linear optimization
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Bibliographic record
Abstract
Primal-dual interior-point methods (IPMs) have shown their power in solving large classes of optimization problems. However, at present there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results, with respect to the strategies of updating the duality gap parameter in the algorithm. The so-called small-update IPMs enjoy the best known theoretical worst-case iteration bound but work very poorly in practice, while the so-called large-update IPMs have superior practical performance but with relatively weaker theoretical results. In this article, by restricting us to linear optimization (LO), we first exploit some interesting properties of a self-regular proximity function, proposed recently by the authors of this work and Roos, and use it to define a neighborhood of the central path. These simple but interesting properties of the proximity function indicate that, when the current iterate is in a large neighborhood of the central path, then the large-update IPM emerges to be the only natural choice. Then, we apply these results to design a specific self-regularity based IPM. Among others, we show that this self-regularity based IPM can also predict precisely the change of the duality gap as the standard IPM does. Therefore, we can directly apply the modified IPM to the simplified self-dual homogeneous model for LO. This provides a remedy for an implementation issue of the new self-regular IPMs. A dynamic large-update IPM in large neighborhood is proposed. Different from traditional large-update IPMs, the new dynamic IPM always takes large-updates and does not utilize any inner iteration to get centered. An worst-case iteration bound of the algorithm is established.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.006 | 0.000 |
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 it