A smoothing-regularization method for mathematical programs with cardinality constraints
Bibliographic record
Abstract
A cardinality constraint in an optimization problem limits the number of nonzeroentries in each element of the solution set. Traditional methods, such as branch-andbound,can reduce the number of feasible points to search. That said, many ofthe proposed methods to solve mathematical programs with cardinality constraintsstill have a computational complexity which is exponential. Previous work has reformulatedcardinality constrained mathematical programs (with dierentiable constraintsand objectives) as mathematical programs with complementarity constraints(MPCCs) which preserve the global and local minimizers of the original problem.Similar to previous work with MPCCs, this gave way to regularization approacheswhich allow standard NLP solvers to be eectively used. In Chapters 3, we investigatethe theoretical properties of a new regularization approach by considering itsconvergence properties. Additionally, Chapter 4 uses the regularization approachto solve a cardinality constrained non-convex objective function. In doing this, wefurther improve on the numerical understandings of the Scholtes-type regularizationapproach while demonstrating that regularization can be eectively employed evenwith a non-convex objective
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".