On the convergence of an alternating direction penalty method for nonconvex problems
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Bibliographic record
Abstract
This paper investigates convergence properties of scalable algorithms for nonconvex and structured optimization. We consider a method that is adapted from the classic quadratic penalty function method, the Alternating Direction Penalty Method (ADPM). Unlike the original quadratic penalty function method, in which single-step optimizations are adopted, ADPM uses alternating optimization, which in turn is exploited to enable scalability of the algorithm. A special case of ADPM is a variant of the well known Alternating Direction Method of Multipliers (ADMM), where the penalty parameter is increased to infinity. We show that due to the increasing penalty, the ADPM asymptotically reaches a primal feasible point under mild conditions. Moreover, we give numerical evidence that demonstrates the potential of the ADPM for computing local optimal points when the penalty is not updated too aggressively.
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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 | 0.000 |
| Science and technology studies | 0.000 | 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