Existence results and optimization over the set of efficient solutions in vector-valued approximation theory
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Bibliographic record
Abstract
Continuity of the objective functions and compactness of their domain are classical assumptions widely used to obtain existence results for solutions of optimization problems.Due to the lack of compactness in general spaces, under some moderate assumptions concerning the objective function and the feasible set, we derive existence results for vector-valued optimization problems and corresponding results for associated scalarized problems in this paper.Furthermore, we apply our results to special vector-valued approximation problems, especially to multi-objective location problems where the whole set of efficient solutions can be generated by a geometric primal-dual algorithm.Moreover, by using the nonlinear scalarizing functional introduced by Gerstewitz, we perform an optimization according to the preferences of a decision maker on the generated set of efficient solutions from which we derive a single solution of this set that corresponds to the preferences of the decision maker.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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