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Record W1545380151 · doi:10.1002/9781118884003.ch2

Optimization algorithms—an overview

2014· other· en· W1545380151 on OpenAlexaff
John C. Nash

Bibliographic record

Venuenot available
Typeother
Languageen
FieldMathematics
TopicAdvanced Optimization Algorithms Research
Canadian institutionsUniversity of Ottawa
Fundersnot available
KeywordsHessian matrixConjugate gradient methodNewton's methodFocus (optics)Newton's method in optimizationGradient descentPoint (geometry)Computer scienceQuasi-Newton methodGaussAlgorithmMathematicsFunction (biology)MinificationMathematical optimizationNonlinear conjugate gradient methodNonlinear systemApplied mathematicsIterative methodLocal convergenceArtificial intelligenceGeometry

Abstract

fetched live from OpenAlex

This chapter focuses on the methods that are developed to try to solve the optimization problem before discussing R's particular tools for such tasks. The original focus of the newton's methods is on finding the roots of functions, and the optimization version attempts to provide the step toward the minimum by approximately solving for the point at which the gradient will be zero. Newton's method is attractive because there are theoretical results that show it is extremely efficient under some conditions. The fundamental chore in Newton's method is computing the Hessian H. The author tries to approximate H in ways that are easier to compute with the Gauss–Newton method. It can be argued that the most effective approach is the family of algorithms called quasi-Newton methods. A different approach to gradient-based function minimization is the family of nonlinear conjugate gradient minimizers.

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 imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.004
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Review · Consensus signal: Review
Teacher disagreement score0.012
Threshold uncertainty score0.039

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.004
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0030.005
Science and technology studies0.0010.001
Scholarly communication0.0030.004
Open science0.0020.002
Research integrity0.0020.004
Insufficient payload (model declined to judge)0.0120.011

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 head0.123
GPT teacher head0.424
Teacher spread0.301 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designNot applicable
Domainnot available
GenreReview

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".

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Citations1
Published2014
Admission routes1
Has abstractyes

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