An Interior-Point/Cutting-Plane Algorithm to Solve the Dual Unit Commitment Problem — on Dual Variables, Duality Gap, and Cost Recovery
Bibliographic record
Abstract
In this chapter, we use an interior-point/cutting-plane (IP/CP) method for non-differentiable optimization to solve the dual to a unit commitment (UC) problem. The IP/CP method has two advantages over previous approaches, such as the sub-gradient and bundle methods: first, it has proved to have better convergence characteristics in an actual implementation; and second, it does not suffer from the parameter-tuning drawback. The results of performance tests using systems with up to 104 units confirm the superiority of the IP/CP method over previous approaches to solve the dual UC problem. We discuss issues that have influenced whether or not UC models are used as the clearing mechanism in electricity markets; these issues include duality gap, cost recovery, and the existence of multiple solutions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.000 | 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; both teacher heads agree on what is shown here.
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".