Nonsmooth generalized complementarity asunconstrained optimization
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Bibliographic record
Abstract
We consider generalized complementarity problem GCP$(f,g)$ when theunderlying functions $f$ and $g$ are $H$-differentiable. Wedescribe $H$-differentials of some GCP functions and theirmerit functions. We give some conditions on the $H$-differentialsof the given functions under which minimizing a merit functioncorresponding to such functions leads to a solution of thegeneralized complementarity problem. Further, we give someconditions on the functions $f$ and $g$ to get a solution ofGCP$(f,g)$ by introducing the concepts of relative monotonicity andP0-property and their variants. Our results further give aunified/generalization treatment of such results for the nonlinearcomplementarity problem when the underlying function is $C^1$ ,semismooth, and locally Lipschitzian.
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Full frame distilled prediction
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it