Characterization of convexifiable functions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract A necessary and sufficient condition is given for a continuous function to be convexified, i.e., decomposed into the sum of a convex and a quadratic concave function. The class of smooth convexifiable functions is large. It includes all the continuously differentiable functions with derivatives satisfying the Lipschitz property, all twice continuously differentiable functions, and all analytic functions. The convexifiable functions are important in mathematical programming: Here we show that every program with such functions can be reduced to a partly linear-convex canonical form by the Liu–Floudas transformation. Hence, loosely speaking, almost all smooth programs of practical interest can be studied using only linear and convex programming, and the relationships between them. Keywords: Convexifiable functionMid-point convexityIntegral mean-value theoremLiu–Floudas transformationGlobal optimumKeywords: 2000 Mathematics Subject Classifications:2000 Mathematics Subject Classifications: 90C3090C31 Acknowledgment The author is indebted to the referee for pointing out various ambiguities in the original version of the article and for drawing attention to the reference Citation11.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| 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) | 0.001 | 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