Proximal point algorithm, Douglas-Rachford algorithm and alternating\n projections: a case study
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Many iterative methods for solving optimization or feasibility problems have\nbeen invented, and often convergence of the iterates to some solution is\nproven. Under favourable conditions, one might have additional bounds on the\ndistance of the iterate to the solution leading thus to worst case estimates,\ni.e., how fast the algorithm must converge.\n Exact convergence estimates are typically hard to come by. In this paper, we\nconsider the complementary problem of finding best case estimates, i.e., how\nslow the algorithm has to converge, and we also study exact asymptotic rates of\nconvergence. Our investigation focuses on convex feasibility in the Euclidean\nplane, where one set is the real axis while the other is the epigraph of a\nconvex function. This case study allows us to obtain various convergence rate\nresults. We focus on the popular method of alternating projections and the\nDouglas-Rachford algorithm. These methods are connected to the proximal point\nalgorithm which is also discussed. Our findings suggest that the\nDouglas-Rachford algorithm outperforms the method of alternating projections in\nthe absence of constraint qualifications. Various examples illustrate the\ntheory.\n
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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