A Study of One-Parameter Regularization Methods for Mathematical\n Programs with Vanishing Constraints
Bibliographic record
Abstract
Mathematical programs with vanishing constraints (MPVCs) are a class of\nnonlinear optimization problems with applications to various engineering\nproblems such as truss topology design and robot motion planning. MPVCs are\ndifficult problems from both a theoretical and numerical perspective: the\ncombinatorial nature of the vanishing constraints often prevents standard\nconstraint qualifications and optimality conditions from being attained;\nmoreover, the feasible set is inherently nonconvex, and often has no interior\naround points of interest. In this paper, we therefore study and compare four\nregularization methods for the numerical solution of MPVCS. Each method depends\non a single regularization parameter, which is used to embed the original MPVC\ninto a sequence of standard nonlinear programs. Convergence results for these\nmethods based on both exact and approximate stationary of the subproblems are\nestablished under weak assumptions. The improved regularity of the subproblems\nis studied by providing sufficient conditions for the existence of KKT\nmultipliers. Numerical experiments, based on applications in truss topology\ndesign and an optimal control problem from aerothermodynamics, complement the\ntheoretical analysis and comparison of the regularization methods. The\ncomputational results highlight the benefit of using regularization over\napplying a standard solver directly, and they allow us to identify two\npromising regularization schemes.\n
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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 | 0.003 | 0.008 |
| 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 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".