A Restricted Dual Peaceman-Rachford Splitting Method for a Strengthened DNN Relaxation for QAP
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Bibliographic record
Abstract
Splitting methods in optimization arise when one can divide an optimization problem into two or more simpler subproblems. They have proven particularly successful for relaxations of problems involving discrete variables. We revisit and strengthen splitting methods for solving doubly nonnegative relaxations of the particularly difficult, NP-hard quadratic assignment problem. We use a modified restricted contractive splitting method approach. In particular, we show how to exploit redundant constraints in the subproblems. Our strengthened bounds exploit these new subproblems and new dual multiplier estimates to improve on the bounds and convergence results in the literature. Summary of Contribution: In our paper, we consider the quadratic assignment problem (QAP). It is one of the fundamental combinatorial optimization problems in the fields of optimization and operations research and includes many fundamental applications. We revisit and strengthen splitting methods for solving doubly nonnegative (DNN) relaxation of the QAP. We use a modified restricted contractive splitting method. We obtain strengthened bounds from improved lower and upper bounding techniques, and in fact, we solve many of these NP-hard problems to (provable) optimality, thus illustrating both the strength of the DNN relaxation and our new bounding techniques.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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