Weak and linear convergence of a generalized proximal point algorithm with alternating inertial steps for a monotone inclusion problem
Bibliographic record
Abstract
The proximal point algorithm (PPA) is a powerful tool for solving monotone inclusion problems.Recently, Tao and Yuan [On the optimal linear convergence rate of a generalized proximal point algorithm, J. Sci.Comput.74 (2018), 826-850] proposed a generalized PPA (GPPA) for finding a zero point of a maximal monotone operator, and obtained the linear convergence rate of the generalized PPA.In this paper, we consider accelerating the GPPA with the aid of the inertial extrapolation.We propose a generalized proximal point algorithm with alternating inertial steps solving monotone inclusion problem, and obtain weak convergence results under some mild conditions.When the inverse of the involved monotone operator is Lipschitz continuous at the origin, we prove that the iterative sequence generated by our generalized proximal point algorithm is linearly convergent.The Fejér monotonicity of even subsequences of the iterative sequence is also recovered.Finally, we give some priori and posteriori error estimates of our generated sequences.
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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 | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".