Less is more: Simplified Nelder-Mead method for large unconstrained optimization
Bibliographic record
Abstract
Nelder-Mead method (NM) for solving continuous non-linear optimization problem is probably the most cited and the most used method in the optimization literature and in practical applications, too. It belongs to the direct search methods, those which do not use the first and the second order derivatives. The popularity of NM is based on its simplicity. In this paper we propose even more simple algorithm for larger instances that follows NM idea. We call it Simplified NM (SNM): instead of generating all n + 1 simplex points in Rn, we perform search using just q + 1 vertices, where q is usually much smaller than n. Though the results cannot be better than after performing calculations in n+1 points as in NM, significant speed-up allows to run many times SNM from different starting solutions, usually getting better results than those obtained by NM within the same cpu time. Computational analysis is performed on 10 classical convex and non-convex instances, where the number of variables n can be arbitrarily large. The obtained results show that SNM is more effective than the original NM, confirming that LIMA yields good results when solving a continuous optimization problem.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".