Relaxed inertial method for solving a class of bilevel variational inequalities
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Bibliographic record
Abstract
In this paper, we investigate a problem of monotone variational inequalities over the solution set of a split variational inequality problem in real Hilbert spaces.We propose a new two-step inertial iterative method with self-adaptive step sizes for approximating the solution of the problem.Our proposed algorithm does not require the co-coerciveness of the associated single-valued operators.Moreover, some parameters are relaxed to accommodate a larger range of values for the step sizes.We obtain strong convergence results under some mild conditions on the control parameters and without prior knowledge of the transformation operators and the monotone and Lipschitz continuous constants of the involved operators.Finally, we apply our result to the traffic network models and we present several numerical experiments to demonstrate the implementability of the proposed method.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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