Inexact alternating direction method of multipliers (InADMM) for the acceleration of l2−l1 inverse problems
Bibliographic record
Abstract
This paper develops and studies an improved version of the Alternating Direction Method of Multipliers (ADMM), named Inexact ADMM (InADMM), specifically designed for largescale optimization problems. The traditional implementation of ADMM can be challenging when applied to large-scale problems. The latter is particularly true in several largescale seismic applications. One subproblem, the x-update, entails solving a large system of equations in each iteration of the ADMM solver. This research addresses two fundamental questions: the precision required in solving the aforementioned linear system of equations at each nested iteration for assured global convergence and the optimal number of nested iterations. InADMM introduces a novel inexactness criterion based on the structure of the problem. This critical modification automates and streamlines the resolution of nested iterations. We demonstrate the application of InADMM with two classical problems in seismic processing and inversion.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".