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Record W2152362622 · doi:10.13140/rg.2.2.14344.01289

Symbolic Convex Analysis

2005· dissertation· en· W2152362622 on OpenAlexfundno aff
Christopher Howard Hamilton

Bibliographic record

VenueSummit (Simon Fraser University) · 2005
Typedissertation
Languageen
FieldMathematics
TopicAdvanced Optimization Algorithms Research
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaSimon Fraser University
KeywordsConvex analysisProper convex functionConic optimizationConvex optimizationMathematical optimizationRegular polygonComputer scienceEllipsoid methodDimension (graph theory)Optimization problemTheoretical computer scienceVisualizationMathematicsArtificial intelligencePure mathematics

Abstract

fetched live from OpenAlex

Convex optimization is a branch of mathematics dealing with non-linear optimization problems with additional geometric structure.This area has been the focus of considerable research due to the fact that convex optimization problems are scalable and can be efficiently solved by interior-point methods.Over the last ten years or so, convex optimization has found applications in many new areas including control theory, signal processing, communications and networks, circuit design, data analysis and finance.As with any new problem, of key concern is visualization of the problem space in order to develop intuition.In this thesis we develop tools for the visualization of convex functions.An important operation in convex optimization is that of Fenchel conjugation.Earlier research has developed algorithms for the symbolic Fenchel conjugation in one dimension, or many separable dimensions.In this thesis these algorithms are extended to work in the non-separable many dimensional case.and my supervisor, Dr. Jonathan Borwein, for his invaluable

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)0.001
metaresearch head score (Gemma)0.006
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: none
Teacher disagreement score0.015
Threshold uncertainty score0.051

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.006
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.002
Science and technology studies0.0010.003
Scholarly communication0.0030.002
Open science0.0010.002
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0150.007

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 head0.023
GPT teacher head0.297
Teacher spread0.274 · 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 designTheoretical or conceptual
Domainnot available
GenreOther

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".

Quick stats

Citations9
Published2005
Admission routes1
Has abstractyes

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