Global optimization under nonlinear constraints based on apollonius fill

Julong Song; Xiangjian He; Zhenxian Lin

doi:10.1109/ICNC.2007.405

Global optimization under nonlinear constraints based on apollonius fill

Julong Song, Xiangjian He, Zhenxian Lin

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

Abstract

Making use of Apollonius Fill, an algorithm is presented, which is for finding solutions of global optimization problems nonlinearly constrained by a circular region in the plane. Using this algorithm, global optimum can be computed fast and precisely. We request no more than first order derivatives of objective functions for the optimization algorithm. If we do not care about the processing time taken, for any given objective function, the global optimum can be obtained as precisely as requested. The proof of convergence of this algorithm is also given in this paper. We use a few numerical examples to show that this algorithm is effective, reliable, and hence is valuable in practice.

Original language	English
Title of host publication	Proceedings - Third International Conference on Natural Computation, ICNC 2007
Pages	39-43
Number of pages	5
DOIs	https://doi.org/10.1109/ICNC.2007.405
Publication status	Published - 2007
Externally published	Yes
Event	3rd International Conference on Natural Computation, ICNC 2007 - Haikou, Hainan, China Duration: 24 Aug 2007 → 27 Aug 2007

Publication series

Name	Proceedings - Third International Conference on Natural Computation, ICNC 2007
Volume	5

Conference

Conference	3rd International Conference on Natural Computation, ICNC 2007
Country/Territory	China
City	Haikou, Hainan
Period	24/08/07 → 27/08/07

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Modelling and Simulation

Access to Document

10.1109/ICNC.2007.405

Cite this

@inproceedings{33511a1c3582413690f98630796d2337,

title = "Global optimization under nonlinear constraints based on apollonius fill",

abstract = "Making use of Apollonius Fill, an algorithm is presented, which is for finding solutions of global optimization problems nonlinearly constrained by a circular region in the plane. Using this algorithm, global optimum can be computed fast and precisely. We request no more than first order derivatives of objective functions for the optimization algorithm. If we do not care about the processing time taken, for any given objective function, the global optimum can be obtained as precisely as requested. The proof of convergence of this algorithm is also given in this paper. We use a few numerical examples to show that this algorithm is effective, reliable, and hence is valuable in practice.",

author = "Julong Song and Xiangjian He and Zhenxian Lin",

year = "2007",

doi = "10.1109/ICNC.2007.405",

language = "English",

isbn = "0769528759",

series = "Proceedings - Third International Conference on Natural Computation, ICNC 2007",

pages = "39--43",

booktitle = "Proceedings - Third International Conference on Natural Computation, ICNC 2007",

note = "3rd International Conference on Natural Computation, ICNC 2007 ; Conference date: 24-08-2007 Through 27-08-2007",

}

Song, J, He, X & Lin, Z 2007, Global optimization under nonlinear constraints based on apollonius fill. in Proceedings - Third International Conference on Natural Computation, ICNC 2007., 4305011, Proceedings - Third International Conference on Natural Computation, ICNC 2007, vol. 5, pp. 39-43, 3rd International Conference on Natural Computation, ICNC 2007, Haikou, Hainan, China, 24/08/07. https://doi.org/10.1109/ICNC.2007.405

Global optimization under nonlinear constraints based on apollonius fill. / Song, Julong; He, Xiangjian; Lin, Zhenxian.
Proceedings - Third International Conference on Natural Computation, ICNC 2007. 2007. p. 39-43 4305011 (Proceedings - Third International Conference on Natural Computation, ICNC 2007; Vol. 5).

Research output: Chapter in Book/Conference proceeding › Conference contribution › peer-review

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AU - He, Xiangjian

AU - Lin, Zhenxian

PY - 2007

Y1 - 2007

N2 - Making use of Apollonius Fill, an algorithm is presented, which is for finding solutions of global optimization problems nonlinearly constrained by a circular region in the plane. Using this algorithm, global optimum can be computed fast and precisely. We request no more than first order derivatives of objective functions for the optimization algorithm. If we do not care about the processing time taken, for any given objective function, the global optimum can be obtained as precisely as requested. The proof of convergence of this algorithm is also given in this paper. We use a few numerical examples to show that this algorithm is effective, reliable, and hence is valuable in practice.

AB - Making use of Apollonius Fill, an algorithm is presented, which is for finding solutions of global optimization problems nonlinearly constrained by a circular region in the plane. Using this algorithm, global optimum can be computed fast and precisely. We request no more than first order derivatives of objective functions for the optimization algorithm. If we do not care about the processing time taken, for any given objective function, the global optimum can be obtained as precisely as requested. The proof of convergence of this algorithm is also given in this paper. We use a few numerical examples to show that this algorithm is effective, reliable, and hence is valuable in practice.

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SN - 9780769528755

T3 - Proceedings - Third International Conference on Natural Computation, ICNC 2007

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BT - Proceedings - Third International Conference on Natural Computation, ICNC 2007

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ER -

Global optimization under nonlinear constraints based on apollonius fill

Abstract

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Conference

ASJC Scopus subject areas

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