A mixed approach for nonlinear equations based on simple smooth penalty function and filled function

Weixiang Wang; Youlin Shang; Liansheng Zhang

doi:10.1117/12.836876

A mixed approach for nonlinear equations based on simple smooth penalty function and filled function

Weixiang Wang^*, Youlin Shang, Liansheng Zhang

^*Corresponding author for this work

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

Abstract

In the paper, we proposed a novel mixed approach for system of nonlinear equations based on simple smooth penalty function method and filled function method. First, we transform the problem of nonlinear equations into a global optimization problem. Then, we use the filled function method to minimize the constructed simple smooth penalty function. Under some mild assumptions, we can get a global optimizer of the penalty problem if the penalty parameter is sufficiently large. By this way, a root of the system of nonlinear equations can be obtained.

Original language	English
Title of host publication	PIAGENG 2009 - Intelligent Information, Control, and Communication Technology for Agricultural Engineering
DOIs	https://doi.org/10.1117/12.836876
Publication status	Published - 2009
Externally published	Yes
Event	PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering - Zhangjiajie, China Duration: 11 Jul 2009 → 12 Jul 2009

Publication series

Name	Proceedings of SPIE - The International Society for Optical Engineering
Volume	7490
ISSN (Print)	0277-786X

Conference

Conference	PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering
Country/Territory	China
City	Zhangjiajie
Period	11/07/09 → 12/07/09

Keywords

Filled function method
Global optimization
Simple smooth exact penalty function method
System of nonlinear equation

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10.1117/12.836876

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Wang, W., Shang, Y., & Zhang, L. (2009). A mixed approach for nonlinear equations based on simple smooth penalty function and filled function. In PIAGENG 2009 - Intelligent Information, Control, and Communication Technology for Agricultural Engineering Article 749017 (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 7490). https://doi.org/10.1117/12.836876

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title = "A mixed approach for nonlinear equations based on simple smooth penalty function and filled function",

abstract = "In the paper, we proposed a novel mixed approach for system of nonlinear equations based on simple smooth penalty function method and filled function method. First, we transform the problem of nonlinear equations into a global optimization problem. Then, we use the filled function method to minimize the constructed simple smooth penalty function. Under some mild assumptions, we can get a global optimizer of the penalty problem if the penalty parameter is sufficiently large. By this way, a root of the system of nonlinear equations can be obtained.",

keywords = "Filled function method, Global optimization, Simple smooth exact penalty function method, System of nonlinear equation",

author = "Weixiang Wang and Youlin Shang and Liansheng Zhang",

year = "2009",

doi = "10.1117/12.836876",

language = "English",

isbn = "9780819478016",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

booktitle = "PIAGENG 2009 - Intelligent Information, Control, and Communication Technology for Agricultural Engineering",

note = "PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering ; Conference date: 11-07-2009 Through 12-07-2009",

}

Wang, W, Shang, Y & Zhang, L 2009, A mixed approach for nonlinear equations based on simple smooth penalty function and filled function. in PIAGENG 2009 - Intelligent Information, Control, and Communication Technology for Agricultural Engineering., 749017, Proceedings of SPIE - The International Society for Optical Engineering, vol. 7490, PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering, Zhangjiajie, China, 11/07/09. https://doi.org/10.1117/12.836876

A mixed approach for nonlinear equations based on simple smooth penalty function and filled function. / Wang, Weixiang; Shang, Youlin; Zhang, Liansheng.
PIAGENG 2009 - Intelligent Information, Control, and Communication Technology for Agricultural Engineering. 2009. 749017 (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 7490).

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

TY - GEN

T1 - A mixed approach for nonlinear equations based on simple smooth penalty function and filled function

AU - Wang, Weixiang

AU - Shang, Youlin

AU - Zhang, Liansheng

PY - 2009

Y1 - 2009

N2 - In the paper, we proposed a novel mixed approach for system of nonlinear equations based on simple smooth penalty function method and filled function method. First, we transform the problem of nonlinear equations into a global optimization problem. Then, we use the filled function method to minimize the constructed simple smooth penalty function. Under some mild assumptions, we can get a global optimizer of the penalty problem if the penalty parameter is sufficiently large. By this way, a root of the system of nonlinear equations can be obtained.

AB - In the paper, we proposed a novel mixed approach for system of nonlinear equations based on simple smooth penalty function method and filled function method. First, we transform the problem of nonlinear equations into a global optimization problem. Then, we use the filled function method to minimize the constructed simple smooth penalty function. Under some mild assumptions, we can get a global optimizer of the penalty problem if the penalty parameter is sufficiently large. By this way, a root of the system of nonlinear equations can be obtained.

KW - Filled function method

KW - Global optimization

KW - Simple smooth exact penalty function method

KW - System of nonlinear equation

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M3 - Conference contribution

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SN - 9780819478016

T3 - Proceedings of SPIE - The International Society for Optical Engineering

BT - PIAGENG 2009 - Intelligent Information, Control, and Communication Technology for Agricultural Engineering

T2 - PIAGENG 2009: Intelligent Information, Control, and Communication Technology for Agricultural Engineering

Y2 - 11 July 2009 through 12 July 2009

ER -

A mixed approach for nonlinear equations based on simple smooth penalty function and filled function

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Keywords

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