Stability on parametric strong symmetric quasi-equilibrium problems via nonlinear scalarization
Bibliographic record
Abstract
This paper focuses on the stability analysis of a class of parametric strong symmetric quasiequilibrium problems (PSSQEP) via scalarization approaches. Based on the oriented distance function, a new nonlinear scalarization function which can separate sets {0} and -C\{0} is presented. By virtue of the scalarization function, a new form of scalar parametric strong symmetric quasi-equilibrium problem (PSSQEP) is obtained, and the union relation between the solution set of (PSSQEP) and the solution sets of a series of (PSSQEP) is established. Finally, the sufficient conditions of the Bergesemicontinuity of solution mappings for (PSSQEP) are obtained via the union relation and the nonlinear scalarization technique, which is different from the scalarization method recently announced. Some interesting examples are given to illustrate the main results.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".