Iteration Complexity of a Proximal Augmented Lagrangian Method for Solving Nonconvex Composite Optimization Problems with Nonlinear Convex Constraints
Bibliographic record
Abstract
This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving constrained nonconvex composite optimization problems, where the constraints are smooth and convex with respect to the order given by a closed convex cone. Each NL-IAPIAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient method followed by a Lagrange multiplier update. Under some mild assumptions, a complexity bound for NL-IAPIAL to obtain an approximate stationary solution of the problem is also derived. Numerical experiments are also given to illustrate the computational efficiency of the proposed method. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grant PGSD3-516700-2018]; Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 312559/2019-4]; Fundação de Amparo à Pesquisa do Estado de Goiás; Office of Naval Research [Grant N00014-18-1-2077]; Exascale Computing Project [Grant 17-SC-20-SC]; Air Force Office of Scientific Research [Grant FA9550-22-1-0088]; UT-Battelle, LLC [Grant DE-AC05-00OR22725].
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".