An Improved Primal Simplex Algorithm for Degenerate Linear Programs
Bibliographic record
Abstract
Since its appearance in 1947, the primal simplex algorithm has been one of the most popular algorithms for solving linear programs. It is often very efficient when there is very little degeneracy, but it often struggles in the presence of high degeneracy, executing many pivots without improving the objective function value. In this paper, we propose an improved primal simplex algorithm that deals with this issue. This algorithm is based on new theoretical results that shed light on how to reduce the negative impact of degeneracy. In particular, we show that, from a nonoptimal basic solution with p positive-valued variables, there exists a sequence of at most m - p + 1 simplex pivots that guarantee the improvement of the objective value, where m is the number of constraints in the linear program. These pivots can be identified by solving an auxiliary linear program. Finally, we briefly summarize computational results that show the effectiveness of the proposed algorithm on degenerate linear programs.
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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) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| 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".