The Analytic Center Cutting Plane Method with Semidefinite Cuts
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Bibliographic record
Abstract
We analyze an analytic center cutting plane algorithm for convex feasibility problems with semidefinite cuts. The problem of interest seeks a feasible point in a bounded convex set, which contains a full-dimensional ball with $\varepsilon$ $(<1)$ radius and is contained in a compact convex set described by matrix inequalities, known as the set of localization. At each iteration, an approximate analytic center of the set of localization is computed. If this point is not in the solution set, an oracle is called to return a p-dimensional semidefinite cut. The set of localization is then updated by adding the semidefinite cut through the center. We prove that the analytic center is recovered after adding a pk-dimensional semidefinite cut in O(pk log(pk+1)) damped Newton's iteration and that the algorithmstops with a point in the solution set when the dimension of the accumulated block diagonal cut matrix reaches the bound of $O^*(\frac{p^2m^3}{{\mu^2\varepsilon}^2})$, where p is the maximum dimension of the cut matrices and $\mu>0$ is a condition number of the field of cuts.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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