An RLT approach for solving the binary-constrained mixed linear complementarity problem
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Bibliographic record
Abstract
It is well known that the mixed linear complementarity problem can be used to model equilibria in energy markets as well as a host of other engineering and economic problems. The binary-constrained, mixed linear complementarity problem is a formulation of the mixed linear complementarity problem in which some variables are restricted to be binary. This paper presents a novel approach for solving the binary-constrained mixed linear complementarity problem. First we solve a series of linear optimization problems that enables us to replace some of the complementarity constraints with linear equations. Then we solve an equivalent mixed integer linear programming formulation of the original binary-constrained mixed, linear complementarity problem (with a smaller number of complementarity constraints) to guarantee a solution to the problem. Our computational results on a wide range of test problems, including some engineering examples, demonstrate the usefulness and the effectiveness of this novel approach.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it