Sensitivity Analysis In Linear And Convex Quadratic Optimization: Invariant Active Constraint Set And Invariant Set Intervals<sup>*</sup>
Bibliographic record
Abstract
Support set invariancy sensitivity analysis is concerned with the finding the range of parameter variation so thai the perturbed problem has still an optimal solution with the same support set that Ihe given optimal solution of the unperturbed problem has. This type of sensitivity analysis in linear and convex quadratic optimization has been recently studied by Ghaffari and Terlaky by restricting their interest on finding this range for primal optimal solutions of Ihese problems. They referred to the range of the parameter as inviiriant support set interval.In this paper, we consider the question: "what the range of the parameter is. where for each parameter value in this range, a dual t)ptinial solution exists with exactly the same set of positive dual slack variables as for the current dual optimal solution.'". Further, the concept of invariant set interval is introduced that is the parameter range, where both the primal variable and the dual slack variable in an optimal solution for each parameter value have invariant support .sets. We present computational methods to identify these intervals and investigate their interrelationship.
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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 | 0.006 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".