Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case
Bibliographic record
Abstract
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized / regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.Regarding superiorization, the state of the art is examined for this problem class, and a novel approach is proposed that employs proximal mappings and is structurally similar to the established forward-backward optimization approach.Regarding convex optimization, accelerated forward-backward splitting with inexact proximal maps is worked out and applied to both the natural splitting least-squares term / regularizer and to the reverse splitting regularizer / least-squares term.Our numerical findings suggest that superiorization can approach the solution of the optimization problem and leads to comparable results at significantly lower costs, after appropriate parameter tuning.On the other hand, applying accelerated forward-backward optimization to the reverse splitting slightly outperforms superiorization, which suggests that convex optimization can approach superiorization too, using a suitable problem splitting.
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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 | 0.003 | 0.009 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".