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Record W2938267440 · doi:10.1287/ijoc.2018.0838

Solving Large Batches of Linear Programs

2019· article· en· W2938267440 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueINFORMS journal on computing · 2019
Typearticle
Languageen
FieldEngineering
TopicOptimization and Mathematical Programming
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsMathematical proofParametric statisticsLinear programmingGeometric programmingBasis (linear algebra)Computer scienceSet (abstract data type)Space (punctuation)MathematicsSensitivity (control systems)Mathematical optimizationAlgorithmGeometry

Abstract

fetched live from OpenAlex

Solving a large batch of linear programs (LPs) with varying parameters is needed in stochastic programming and sensitivity analysis, among other modeling frameworks. Solving the LPs for all combinations of given parameter values, called the brute-force approach, can be computationally infeasible when the parameter space is high-dimensional and/or the underlying LP is computationally challenging. This paper introduces a computationally efficient approach for solving a large number of LPs that differ only in the right-hand side of the constraints ([Formula: see text] of [Formula: see text]). The computational approach builds on theoretical properties of the geometry of the space of critical regions, where a critical region is defined as the set of [Formula: see text]’s for which a basis is optimal. To formally support our computational approach we provide proofs of geometric properties of neighboring critical regions. We contribute to the existing theory of parametric programming by establishing additional results, providing deeper geometric understanding of critical regions. On the basis of the geometric properties of critical regions, we develop an algorithm that solves the LPs in batches by finding critical regions that contain multiple [Formula: see text]’s. Moreover, we suggest a data-driven version of our algorithm that uses the distribution (e.g., shape) of a sample of [Formula: see text]’s for which the LPs need to be solved. We empirically compared our approach and three other methods on various instances. The results show the efficiency of our approach in comparison with the other methods but also indicate some limitations of the algorithm. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0838 .

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: Simulation or modeling
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.368
Threshold uncertainty score0.320

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.012
GPT teacher head0.235
Teacher spread0.224 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it