The connectedness of weakly and strongly efficient solution sets of nonconvex vector equilibrium problems
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Bibliographic record
Abstract
In this paper, we consider nonconvex vector equilibrium problems, and discuss the properties of their efficient solution sets. First, based on the Hiriart-Urruty oriented distance function, we introduce a new nonlinear scalarization function, and study its continuity properties. Then, we propose various concepts of connectedness for a vector-valued mapping, and discuss their relationships. Finally, we use these concepts to study sufficient conditions of the nonemptyness and connectedness of weakly and strongly efficient solution sets of such problems via the scalarization method and/or conditions related to the triangle inequality.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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