Primal-dual partitions in linear semi-infinite programming with bounded coefficients
Bibliographic record
Abstract
We consider two partitions over the space of linear semi-infinite programming parameters with a fixed index set and bounded coefficients (the constraint functions are bounded).The first one is the primal-dual partition inspired by consistency and boundedness of the optimal value of the problem.The second one is a refinement of the primal-dual partition that arises by considering also the boundedness of the optimal set.These two partitions have been studied in the continuous case, i.e., when the set of indices is an infinite compact topological space and the constraint functions are continuous.In this paper, we extend these results to the case in which the constraint functions are bounded, but not necessarily continuous.We study the same primal-dual partitions and characterize the interior of the corresponding cells.Through examples, we show that the conditions characterizing the cells of both partitions in the continuous case are neither necessary nor sufficient when the constraint functions are just bounded.In addition, a sufficient condition for the boundedness of the optimal set of the dual problem is established.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".