On the simultaneous convergence of values and trajectories of continuous inertial dynamics with Tikhonov regularization to solve convex minimization with affine constraints
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Bibliographic record
Abstract
In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve general convex minimization problems with linear constraints.The system is associated with the augmented Lagrangian formulation of a minimization problem.The corresponding dynamic involves three general time-varying parameters, which are respectively associated with viscous damping, extrapolation and temporal scaling.By appropriately adjusting these parameters, each with specific properties, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap.These results naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.
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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 | 0.000 | 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 | 0.000 | 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