An Improved Decomposition Approach and its Computational Technique for Analyzing Primal-Dual Relationship in LP & LFP Problems
Bibliographic record
Abstract
In this paper, we study the methodology of primal dual solutions in Linear Programming (LP) & Linear Fractional Programming (LFP) problems. A comparative study is also made on different duals of LP & LFP. We then develop an improved decomposition approach for showing the relationship of primal and dual approach of LP & LFP problems by giving algorithm. Numerical examples are given to demonstrate our method. A computer programming code is also developed for showing primal and dual decomposition approach of LP & LFP with proper instructions using AMPL. Finally, we have drawn a conclusion stating the privilege of our method of computation. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 65-75 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17660
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".