Vectorial penalisation in vector optimisation in real linear-topological spaces
Bibliographic record
Abstract
The aim of this paper is to present a vectorial penalisation approach for vector optimisation problems in which the vector-valued objective function acts between real linear-topological spaces X and Y , where the image space Y is partially ordered by a pointed convex cone.In essence, the approach replaces the original constrained vector optimisation problem (with not necessarily convex feasible set) by two unconstrained vector optimisation problems, where in one of the two problems a penalisation term (function) with respect to the original feasible set is added to the vector objective function.To derive our main results, we use a generalised convexity (quasiconvexity) notion for vector functions in the sense of Jahn.Our results extend/generalise known results in the context of vectorial penalisation in multiobjective/vector optimisation.We put a special emphasis on the construction of appropriate penalisation functions for several popular classes of (vector) optimisation problems (e.g., semidefinite/copositive programming, second-order cone programming, optimisation in function spaces).
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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 | 0.004 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".