A unified framework of some proximal-based decomposition methods for monotone variational inequalities with separable structures
Bibliographic record
Abstract
Some existing decomposition methods for solving a class of variational inequalities (VIs) with separable structures are closely related to the classical proximal point algorithm (PPA), as their decomposed sub-VIs are regularized by proximal terms. Differing in whether the generated sub-VIs are suitable for parallel computation, these proximal-based methods can be categorized into parallel decomposition methods and alternating decomposition methods. This paper generalizes these methods and thus presents a unified framework of proximal-based decomposition methods for solving this class of VIs, in both exact and inexact versions. Then, for various special cases of the unified framework, we analyze respective strategies for fulfilling a condition that ensures the convergence, which are realized by determining appropriate proximal parameters. Moreover, some concrete numerical algorithms for solving this class of VIs are derived. In particular, the inexact version of this unified framework gives rise to some implementable algorithms that allow the involved sub-VIs to be solved under some favorable criteria developed in PPA literature. © 2012 Yokohama Publishers.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".