Feasibility and Constraint Analysis of Sets of Linear Matrix Inequalities
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Bibliographic record
Abstract
We present a constraint analysis methodology for linear matrix inequality constraints. If the constraint set is found to be feasible, we search for a minimal representation; otherwise, we search for an irreducible infeasible system. The work is based on the solution of a set-covering problem where each row corresponds to a sample point and is determined by constraint satisfaction at the sampled point. Thus, an implementation requires a method to collect points in the ambient space and a constraint oracle. Much of this paper will be devoted to the development of a hit-and-run sampling methodology. Test results confirm that our approach not only provides information required for constraint analysis but will also, if the feasible region has a nonvoid interior, with probability one, find a feasible point.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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)
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