Coordination in Markets With Nonconvexities as a Mathematical Program With Equilibrium Constraints—Part I: A Solution Procedure
Bibliographic record
Abstract
This paper is concerned with developing an algorithm for solving the coordination problem that arises in a new equilibrium model , which for the purpose of this presentation applies to a static (no-time coupling costs or constraints) electricity pool market with price inelastic demand and no network. The new equilibrium model has the following main properties: i) every scheduled generator satisfies its minimum surplus (or bid profit) condition; ii) the energy price is a system marginal cost (Lagrange multiplier associated with the power balance constraint in the related economic dispatch problem where all of the discrete variables are fixed to their optimal values); iii) the power balance and all the generators' technical constraints are satisfied. To solve the coordination problem, which is a subproblem of the new equilibrium model, it is mathematically convenient to cast the former as a three-level nested optimization problem. We substitute the ensuing lower-level subproblems with an equivalent set of explicit algebraic equalities and inequalities. Hence, we obtain a one-level problem, which is a discrete-continuous mathematical program with complementarity or equilibrium constraints (MPEC). Finally, we transform the one-level mathematical program into mixed-integer linear form by substitution of the complementarity terms and the remaining nonlinear terms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".