Bregman ADMM: A new algorithm for nonconvex optimization with linear constraints
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Bibliographic record
Abstract
Alternating direction method of multipliers (ADMM) is a widely used algorithm for solving two-block separable problems with linear constraints.However, its applicability in various fields is limited by the need to assume the global Lipschitz continuity of the gradient of differentiable functions, which is often infeasible in nonconvex optimization problems.To address this limitation, we propose a new version of the Bregman ADMM that can return to the ADMM while avoiding the need for global Lipschitz continuity of the gradient.The Bregman ADMM relaxes the classical ADMM's requirement for global Lipschitz continuous gradient, enriching its applications.We prove that when the associated function satisfies the Kurdyka-ojasiewicz inequality and certain assumptions, the iterative sequence generated by our algorithm converges to a critical point of the problem.Additionally, we analyze the rate of convergence of the algorithm.
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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 | 0.000 |
| 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