A modification piecewise convexification method with a classification strategy for box-constrained non-convex optimization programs
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Bibliographic record
Abstract
This paper presents a piecewise convexification method with a box classification strategy to approximate the entire globally optimal solution set of non-convex optimization problems with box constraints.First, the box classification strategy is proposed based on the convexity of the objective function on the sub-boxes, which helps to reduce the number of box divisions and improve the computational efficiency.At the same time, we construct the piecewise convexification problem of the original nonconvex optimization problem by applying the α-based Branch-and-Bound (αBB) method, and we define the (approximate) solution set of the piecewise convexification problem based on the result of classifying the sub-boxes.Then, it is deduced that the globally optimal solution set can be approximated by the (approximate) solution set of the piecewise convexification problem.Finally, a piecewise convexification algorithm is proposed that includes a new subset selection technique for division and two new termination tests.The results of our experiments demonstrate the effectiveness and general superiority of our approach over the competition.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| 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