($\epsilon$-)efficiency in multicriteria fractional optimization
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Bibliographic record
Abstract
The issue of characterizing completely the efficient (Pareto) solutions to a multicriteria (or multiobjective) fractional minimization problem, when the involved functions are convex, has not been addressed previously in the literature.Thanks to an earlier characterization of weak (-)efficiency in difference vector optimization by El Maghri, a similar condition given in terms of both strong (Fenchel) and weak (Pareto) -subdifferentials is first obtained for general unconstrained multicriteria fractional problems.Next, this condition is extended to constrained problems whose numerators and constraints are convex.When the fractional problem consists of minimizing ratios of convex functions by concave functions, KKT-type vector characterizations are developed for both proper and weak (-)efficiency.Finally, applications to the special all-linear case lead to (-)efficiency criteria given entirely in terms of the data.
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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 | 0.000 | 0.000 |
| 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