A Unified Framework of Regularization Methods for Degenerate Non-Linear Optimization Models
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Bibliographic record
Abstract
In this paper, we study three classes of difficult non-linear optimization, problems with complementarity (MPCC), vanishing (MPVC) and cardinality constraints (OMCC). They all have in common degenerate constraints, which fail to satisfy classical constraint qualifications in a generic way. The feasible sets of these problems are non-convex, possibly non-connected, with an empty relative interior. This causes several difficulties in practice. In a recent work (Dussault et al. 2017), we propose a unified framework of methods that consider a regularization-penalization-active set method to solve the MPCC, which possesses the best-known convergence properties. In this paper, we extend this unified framework to MPVC and OMCC and consider some applications on optimal control problems.
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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 | 0.011 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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