On global optimality conditions for D.C. minimization problems with D.C. constraints
Bibliographic record
Abstract
The paper addresses the nonconvex nonsmooth optimization problem with the cost function, and equality and inequality constraints given by d.c.functions, i.e. represented as a difference of convex functions.The original problem is reduced to a problem without constraints with the help of the exact penalization theory.After that, the penalized problem is represented as a d.c.minimization problem without constraints, for which the new mathematical tools under the form of global optimality conditions (GOCs) are developed.The GOCs reduce the nonconvex problem in question to a family of convex (linearized with respect to the basic nonconvexities) problems.In addition, the GOCs are related to some nonsmooth form of the KKT-theorem for the original problem.Besides, the GOCs possess the constructive (algorithmic) property, which, when the GOCs are broken down, implies the producing of a feasible point that is better (in the original problem) than the one in question.The effectiveness of the GOCs is demonstrated by examples.
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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 | 0.006 | 0.012 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.005 | 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".