Minimax exactness and global saddle points of nonlinear augmented Lagrangians
Bibliographic record
Abstract
We study global minimax exactness of merit functions for constrained optimization problems.This concept arises as a natural generalization of the definition of global saddle points in the unified theory of exactness of penalty and augmented Lagrangian functions.We obtain necessary and sufficient conditions for the global minimax exactness of nonlinear augmented Lagrangians in the form of the localization principle, which allow one to reduce the study of the existence of global saddle points (or the existence of solutions of the augmented dual problem) to a local analysis of sufficient optimality conditions.With the use of the localization principle, we obtain simple necessary and sufficient conditions for the existence of global saddle points of He-Wu-Meng's augmented Lagrangian for inequality constrained problems and nonlinear rescaling Lagrangians for nonconvex semidefinite programs.We also introduce and analyze a new nonlinear smooth augmented Lagrangian for constrained minimax problems and provide necessary and sufficient conditions for the existence of a global saddle point of this augmented Lagrangian, which, in particular, expose some limitations of exponential penalty function methods.
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.
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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".