Log-exponential approximation in semi-infinite programming: A variational approach
Bibliographic record
Abstract
In this paper, we propose an approximation technique for a function which is the supremum of a general family of functions by means of a function, of LogExp-type, involving a finite number of the data functions.A study of variational properties of such an approximating function is carried out in the paper.In particular, the epigraphic convergence of these approximating functions to the supremum function is proven.Moreover, refined calculus specifying the relations among the subdifferentials (regular and general) of the approximating and the data functions are provided in the first part of the paper.In the second part, we propose to approximate a general semi-infinite programming problem by a simple problem with a single constraint.Applying the results of the first part we establish, under standard hypotheses, the convergence of optimal values and solutions of these problems to the corresponding ones of the original problem.The Lagrangian duality of this problem is also studied but restricted to the semi-infinite convex programming problem, and optimal dual solutions are built by means of a sequential procedure.
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How this classification was reachedexpand
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 | 0.002 | 0.004 |
| 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".