Bregman ADMM: A new algorithm for nonconvex optimization with linear constraints
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-Łojasiewicz 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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".