Canonical duality theory for solving nonconvex/discrete constrained global optimization problems

Ning Ruan; David Yang Gao

doi:10.1007/978-3-319-58017-3_9

Canonical duality theory for solving nonconvex/discrete constrained global optimization problems

Ning Ruan, David Yang Gao

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

Abstract

This paper presents a canonical duality theory for solving general nonconvex/discrete constrained minimization problems. By using the canonical dual transformation, these challenging problems can be reformulated as a unified canonical dual problem (i.e., with zero duality gap) in continuous space, which can be solved easily to obtain global optimal solution. Some basic concepts and general theory in canonical systems are reviewed. Applications to Boolean least squares problems are illustrated.

Original language	English
Title of host publication	Canonical Duality Theory
Subtitle of host publication	Unified Methodology for Multidisciplinary Study
Editors	David Yang Gao, Vittorio Vittorio, Ning Ruan
Place of Publication	Cham Switzerland
Publisher	Springer
Chapter	9
Pages	187-201
Number of pages	15
Edition	1st
ISBN (Electronic)	9783319580173
ISBN (Print)	9783319580166
DOIs	https://doi.org/10.1007/978-3-319-58017-3_9
Publication status	Published - 2017
Externally published	Yes

Publication series

Name	Advances in Mechanics and Mathematics
Publisher	Springer
Volume	37
ISSN (Print)	1571-8689
ISSN (Electronic)	1876-9896

Keywords

Canonical Duality
Canonical Dual Problem
Duality Transformation
Nonconvex Mechanics
Total Complementary Function

Access to Document

10.1007/978-3-319-58017-3_9

1 Comment / Debate

Erratum: Canonical duality theory for solving nonconvex/discrete constrained global optimization problems (Mathematics and Mechanics of Solids)
Ruan, N. & Gao, D. Y., 1 Mar 2016, In: Mathematics and Mechanics of Solids. 21, 3, p. NP194-NP205
Research output: Contribution to journal › Comment / Debate › Other › peer-review

2 Citations (Scopus)

Cite this

Ruan, N., & Gao, D. Y. (2017). Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. In D. Yang Gao, V. Vittorio, & N. Ruan (Eds.), Canonical Duality Theory: Unified Methodology for Multidisciplinary Study (1st ed., pp. 187-201). (Advances in Mechanics and Mathematics; Vol. 37). Springer. https://doi.org/10.1007/978-3-319-58017-3_9

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keywords = "Canonical Duality, Canonical Dual Problem, Duality Transformation, Nonconvex Mechanics, Total Complementary Function",

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Ruan, N & Gao, DY 2017, Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. in D Yang Gao, V Vittorio & N Ruan (eds), Canonical Duality Theory: Unified Methodology for Multidisciplinary Study. 1st edn, Advances in Mechanics and Mathematics, vol. 37, Springer, Cham Switzerland, pp. 187-201. https://doi.org/10.1007/978-3-319-58017-3_9

Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. / Ruan, Ning; Gao, David Yang.

Canonical Duality Theory: Unified Methodology for Multidisciplinary Study. ed. / David Yang Gao; Vittorio Vittorio; Ning Ruan. 1st. ed. Cham Switzerland : Springer, 2017. p. 187-201 (Advances in Mechanics and Mathematics; Vol. 37).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

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Ruan N, Gao DY. Canonical duality theory for solving nonconvex/discrete constrained global optimization problems. In Yang Gao D, Vittorio V, Ruan N, editors, Canonical Duality Theory: Unified Methodology for Multidisciplinary Study. 1st ed. Cham Switzerland: Springer. 2017. p. 187-201. (Advances in Mechanics and Mathematics). https://doi.org/10.1007/978-3-319-58017-3_9

Canonical duality theory for solving nonconvex/discrete constrained global optimization problems

Abstract

Publication series

Keywords

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Research output

Erratum: Canonical duality theory for solving nonconvex/discrete constrained global optimization problems (Mathematics and Mechanics of Solids)

Cite this