A proximal bundle algorithm for a class of quasilinear variational inequalities of the second kind arising in the viscoplastic laminar flow
Bibliographic record
Abstract
This paper focuses on the numerical solution of a variational inequality of the second kind, which arises as a model for the laminar flow of a Herschel-Bulkley fluid in the cross-section of a pipe.To tackle this problem, we develop a nonsmooth proximal bundle algorithm that bypasses the need for regularization techniques.We begin by formulating and analyzing an associated nonsmooth and convex optimization problem that characterizes the solution of the variational inequality.Following a discretize-then-optimize approach, we employ a first-order finite element discretization for the objective functional.The core of our method lies in the nonsmooth bundle algorithm, which leverages a Moreau-Yosida approximation combined with a quasi-Newton BFGS update.This approach approximates the function and gradient values through a finite inner bundle algorithm.We build and analyze the proposed algorithm, examining its convergence properties in the context of the flow model.Additionally, we demonstrate its efficiency through both theoretical analysis and numerical experiments.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".