Strong convergent inertial Tseng’s extragradient method for solving non-Lipschitz quasimonotone variational inequalities in Banach spaces
Bibliographic record
Abstract
The class of quasimonotone variational inequalities is more general and applicable than the class of pseudomonotone and monotone variational inequalities. However, few results can be found in the literature on quasimonotone variational inequalities and currently results are mostly on weak convergent methods in the framework of Hilbert spaces. In this paper, we study the class of non-Lipschitz quasimonotone variational inequalities and the class of non-Lipschitz variational inequalities without monotonicity in the framework of Banach spaces. We propose a new inertial Tseng's extragradient method and obtain some strong convergence results for the proposed algorithm under some mild conditions on the control parameters. While the cost operator is non-Lipschitz, our proposed method does not require any linesearch procedure but employs a more efficient and simple self-adaptive step sizes with known parameters. Finally, we present several numerical experiments to demonstrate the implementability of our proposed method.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".