Self-regular proximities and new search directions for nonlinear P*(K) complementarity problems
Bibliographic record
Abstract
We deal with interior point methods (IPMs) for solving a class of so-called P ( ) complementarity problems (CPs). First of all, several elementary results about P ( ) mappings and P ( ) CPs are presented. Then we extend some notions introduced recently by Peng, Roos and Terlaky [22] for linear optimization problems to the case of CPs. New large-update IPMs for solving CPs are introduced based on the so-called self-regular proximities. To build up the complexity of these new algorithms, we impose a new smoothness condition on the underlying mapping and this condition can be viewed as a natural generalization of the relative Lipschitz condition for convex programs introduced by Jarre [6]. By utilizing various appealing properties of self-regular proximities, we will show that if the undertaken problem satis es certain conditions, then these new large-update IPMs for solving CPs have polynomial O n q+1 2q log n iteration bounds where q is the so-called barrier degree of the corresponding proximity. The research of the rst two authors are mainly supported by the project High Performance Methods for Mathematical Optimization under the Dutch SWON-grant 613-304-200. Both the rst and third authors were partially supported by the National Science and Engineering Research Council of Canada, grant # : 227650-00. The work of the last author was supported by Grant-in-Aid for Scienti c Research ((C@)11650064) of the Ministry of Education, Science and Culture of Japan. This work was nished when the rst author visited the third author at the Department of Computing and Software, McMaster University, Canada. Email: pengj@mcmail.mcmaster.ca, J.Peng@its.tudelft.nl.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| 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".