Bibliographic record
Abstract
This dissertation is concerned with the design of branch-and-cut algorithms for a variety of nonconvex nonlinear problems pertaining to power systems operations and planning. By understanding the structure of specific problems, we can leverage powerful commercial optimization solvers designed for convex optimization and mixed-integer programs. The bulk of the work concerns the Alternating Current Optimal Power Flow (ACOPF) problem. The ACOPF problem is to find a minimum cost generation dispatch that will yield flows that can satisfy demand as well as various engineering constraints. A standard formulation can be posed as a nonconvex Quadratically Constrained Quadratic Program with complex variables. We develop a novel spatial branch-and-bound algorithm for generic nonconvex QCQP with bounded complex variables that relies on a semidefinite programming (SDP) relaxation strengthened with linear valid inequalities. ACOPF-specific domain reduction or bound tightening techniques are also introduced to improve the algorithm's convergence rate. We also introduce second-order conic valid inequalities so that any SDP can be outer-approximated with conic quadratic cuts and test the technique on ACOPF. Another application is the incorporation of convex quadratic costs in unit commitment, which is a multi-period electric generation scheduling problem. We show that conic reformulation can both theoretically and practically improve performance on this mixed-integer nonlinear problem. We conclude with methods for approximating a mixed-integer convex exponential constraint. Applications include capital budgeting, the system reliability redundancy problem, and feature subset selection for logistic regression.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 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".