Algorithms for solving optimization programs involving difference of convex functions
Bibliographic record
Abstract
We investigate constrained optimization problems involving difference of convex functions in the objective as well as in the constraint functions.We first associate with the considered problem a parametric convex one.Relations between the two problems are analyzed, and necessary optimality conditions are given for such problems.Using the parametric approach, we propose three kinds of methods.The first one, we call the DC method of centers, generates a sequence of convex problems that incorporate the constraints in their objective functions.The second one is a pure proximal point method, based on the DC method of centers and the proximal point algorithm idea.The third one is a family of proximal bundle methods that combine the previous cited parametric approach, the proximal point algorithm idea, and the bundle concept.These methods are globally convergent in the sense that they converge for every starting point, feasible, or infeasible.We show that every cluster point of the sequence of optimal solutions of these problems satisfies necessary optimality conditions of KKT criticality type.Finally, we end with some numerical tests to illustrate the behavior of the algorithm.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".