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Canonical Duality-Triality Theory for Solving General Global Optimization Problems in Complex Systems

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D. M. Morales Silva, D. Y. Gao

Optimization and Control · Submitted 30 Sep 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics.

how it is stated · asserted 0.75 read the record →

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arXiv ID1210.0180 (version 2)
Pith IDW2VL6UCJ, Pith's permanent record of this paper and its review
CitationD. M. Morales Silva, D. Y. Gao. "Canonical Duality-Triality Theory for Solving General Global Optimization Problems in Complex Systems." arXiv:1210.0180 (2012). https://pith.science/paper/W2VL6UCJ
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,501 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.27 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics. Detailed applications are illustrated by several examples.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 General nonconvex optimization problems are studied by using the canonical duality-triality theory. contribution 0.65 0.77 0.10 asserted 0.99
s1 The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. result 0.61 0.85 0.31 asserted 1.00
s2 This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics. interpretation 0.87 0.63 0.42 asserted 0.75
s3 Detailed applications are illustrated by several examples. contribution 0.54 0.82 0.04 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics. Detailed applications are illustrated by several examples.

Human review

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How the literature uses it

2 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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