Mehrotra-type predictor-corrector algorithm revisited
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Bibliographic record
Abstract
Abstract Motivated by a numerical example that shows that a feasible version of Mehrotra's original predictor-corrector algorithm might be inefficient in practice, Salahi et al. [M. Salahi, J. Peng and T. Terlaky, On Mehrotra-type predictor-corrector algorithms, to apper in SIAM J. Optim.] proposed a so-called safeguard-based variant of the algorithm that enjoys polynomial iteration complexity, although its practical efficiency is preserved. In this paper, we analyse the same Mehrotra's algorithm from a different perspective. We give a condition on the maximum step size in the predictor direction, the violation of which might imply a very small or zero step size in the corrector direction of the algorithm. This might explain the reason for occasional ill behaviour of the feasible version of Mehrotra's original algorithm. We propose to cut the maximum step size in the predictor direction if it is above a certain threshold. If this cut does not give a desirable step size, then we cut it for the second time that allows us to give a lower bound for the step size in the corrector direction. This enables us to prove an 𝒪(n 5/2log (n/ε)) worst case iteration complexity bound for the new algorithm. By slightly modifying the Newton system in the corrector step, we reduce the iteration complexity to 𝒪 (n 3/2log (n/ε)). Finally, we report some illustrative computational results using the McIPM software package.
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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 | 0.001 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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