A Dai-Liao-like projection method for solving convex constrained nonlinear monotone equations and minimizing the $\ell_1$-regularized problem
Bibliographic record
Abstract
In this paper, a three-term derivative-free method for solving a nonlinear system of equations with convex constraints is proposed.In addition, by reformulating an ℓ 1 -regularized problem into a nonlinear system of equations, the proposed method is applicable to solving signal recovery and image deblurring problems.Our method is based on the projection technique of Solodov and Svaiter (1998) by incorporating a quasi-Newton-like direction with the Dai-Liao conjugate gradient parameter.The proposed method is matrix-free and the search direction satisfies a certain descent condition.Under the assumption that the underlying function is monotone and Lipschitzian, the global convergence of the proposed method is established.Preliminary numerical experiments on some large-scale nonlinear system of equations with convex constraints show that the proposed method is efficient.Furthermore, we apply the proposed method to the ℓ 1 -regularization problem in compressive sensing.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".