A new neural network for nonlinear constrained optimization problems

Zhiqing Meng; Chuangyin Dang; Gengui Zhou; Yihua Zhu; Min Jiang

doi:10.1007/978-3-540-28647-9_68

A new neural network for nonlinear constrained optimization problems

Zhiqing Meng^*
, Chuangyin Dang^*
, Gengui Zhou
, Yihua Zhu
, Min Jiang

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

5 Citations (Scopus)

Abstract

In this paper we introduce a new neural network for solving nonlinear constrained optimization problems. The energy function for the neural network with its neural dynamics is obtained from an application of the penalty-function method. We show that the system of the neural network is stable and an equilibrium point of the neural dynamics yields an optimal solution for the corresponding nonlinear constrained optimization problem. Based on the relationship between the equilibrium points and the energy function, an algorithm is developed for computing an equilibrium point of the system or an optimal solution to its optimization problem. The efficiency of the algorithm is demonstrated with several numerical examples. © Springer-Verlag 2004.

Original language	English
Title of host publication	Advances in Neural Networks - ISNN 2004
Subtitle of host publication	International Symposium on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, Part I
Editors	Fu-Liang Yin, Jun Wang, Chengan Guo
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	406-412
ISBN (Electronic)	978-3-540-28647-9
ISBN (Print)	978-3-540-22841-7
DOIs	https://doi.org/10.1007/978-3-540-28647-9_68
Publication status	Published - 2004
Event	International Symposium on Neural Networks (ISNN 2004) - Dalian, China Duration: 19 Aug 2004 → 21 Aug 2004

Publication series

Name	Lecture Notes in Computer Science
Volume	3173
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Symposium on Neural Networks (ISNN 2004)
Abbreviated title	ISNN
Place	China
City	Dalian
Period	19/08/04 → 21/08/04

Research Keywords

Equilibrium point
Hopfield neural networks
Penalty function
Stability

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Meng, Z., Dang, C., Zhou, G., Zhu, Y., & Jiang, M. (2004). A new neural network for nonlinear constrained optimization problems. In F.-L. Yin, J. Wang, & C. Guo (Eds.), Advances in Neural Networks - ISNN 2004: International Symposium on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, Part I (pp. 406-412). (Lecture Notes in Computer Science; Vol. 3173). Springer . https://doi.org/10.1007/978-3-540-28647-9_68

Meng, Zhiqing ; Dang, Chuangyin ; Zhou, Gengui et al. / A new neural network for nonlinear constrained optimization problems. Advances in Neural Networks - ISNN 2004: International Symposium on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, Part I. editor / Fu-Liang Yin ; Jun Wang ; Chengan Guo. Berlin, Heidelberg : Springer , 2004. pp. 406-412 (Lecture Notes in Computer Science).

@inproceedings{7a6aa80018e542bb8c394334f0eb3cba,

title = "A new neural network for nonlinear constrained optimization problems",

abstract = "In this paper we introduce a new neural network for solving nonlinear constrained optimization problems. The energy function for the neural network with its neural dynamics is obtained from an application of the penalty-function method. We show that the system of the neural network is stable and an equilibrium point of the neural dynamics yields an optimal solution for the corresponding nonlinear constrained optimization problem. Based on the relationship between the equilibrium points and the energy function, an algorithm is developed for computing an equilibrium point of the system or an optimal solution to its optimization problem. The efficiency of the algorithm is demonstrated with several numerical examples. {\textcopyright} Springer-Verlag 2004.",

keywords = "Equilibrium point, Hopfield neural networks, Penalty function, Stability",

author = "Zhiqing Meng and Chuangyin Dang and Gengui Zhou and Yihua Zhu and Min Jiang",

year = "2004",

doi = "10.1007/978-3-540-28647-9\_68",

language = "English",

isbn = "978-3-540-22841-7",

series = "Lecture Notes in Computer Science",

publisher = "Springer ",

pages = "406--412",

editor = "Fu-Liang Yin and Jun Wang and Chengan Guo",

booktitle = "Advances in Neural Networks - ISNN 2004",

note = "International Symposium on Neural Networks (ISNN 2004), ISNN ; Conference date: 19-08-2004 Through 21-08-2004",

}

Meng, Z, Dang, C, Zhou, G, Zhu, Y & Jiang, M 2004, A new neural network for nonlinear constrained optimization problems. in F-L Yin, J Wang & C Guo (eds), Advances in Neural Networks - ISNN 2004: International Symposium on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, Part I. Lecture Notes in Computer Science, vol. 3173, Springer , Berlin, Heidelberg, pp. 406-412, International Symposium on Neural Networks (ISNN 2004), Dalian, China, 19/08/04. https://doi.org/10.1007/978-3-540-28647-9_68

A new neural network for nonlinear constrained optimization problems. / Meng, Zhiqing; Dang, Chuangyin; Zhou, Gengui et al.
Advances in Neural Networks - ISNN 2004: International Symposium on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, Part I. ed. / Fu-Liang Yin; Jun Wang; Chengan Guo. Berlin, Heidelberg: Springer , 2004. p. 406-412 (Lecture Notes in Computer Science; Vol. 3173).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - A new neural network for nonlinear constrained optimization problems

AU - Meng, Zhiqing

AU - Dang, Chuangyin

AU - Zhou, Gengui

AU - Zhu, Yihua

AU - Jiang, Min

PY - 2004

Y1 - 2004

N2 - In this paper we introduce a new neural network for solving nonlinear constrained optimization problems. The energy function for the neural network with its neural dynamics is obtained from an application of the penalty-function method. We show that the system of the neural network is stable and an equilibrium point of the neural dynamics yields an optimal solution for the corresponding nonlinear constrained optimization problem. Based on the relationship between the equilibrium points and the energy function, an algorithm is developed for computing an equilibrium point of the system or an optimal solution to its optimization problem. The efficiency of the algorithm is demonstrated with several numerical examples. © Springer-Verlag 2004.

AB - In this paper we introduce a new neural network for solving nonlinear constrained optimization problems. The energy function for the neural network with its neural dynamics is obtained from an application of the penalty-function method. We show that the system of the neural network is stable and an equilibrium point of the neural dynamics yields an optimal solution for the corresponding nonlinear constrained optimization problem. Based on the relationship between the equilibrium points and the energy function, an algorithm is developed for computing an equilibrium point of the system or an optimal solution to its optimization problem. The efficiency of the algorithm is demonstrated with several numerical examples. © Springer-Verlag 2004.

KW - Equilibrium point

KW - Hopfield neural networks

KW - Penalty function

KW - Stability

UR - https://www.scopus.com/pages/publications/24944587249

UR - https://www.scopus.com/pages/publications/24944587249#tab=impact

U2 - 10.1007/978-3-540-28647-9_68

DO - 10.1007/978-3-540-28647-9_68

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 978-3-540-22841-7

T3 - Lecture Notes in Computer Science

SP - 406

EP - 412

BT - Advances in Neural Networks - ISNN 2004

A2 - Yin, Fu-Liang

A2 - Wang, Jun

A2 - Guo, Chengan

PB - Springer

CY - Berlin, Heidelberg

T2 - International Symposium on Neural Networks (ISNN 2004)

Y2 - 19 August 2004 through 21 August 2004

ER -

Meng Z, Dang C, Zhou G, Zhu Y, Jiang M. A new neural network for nonlinear constrained optimization problems. In Yin FL, Wang J, Guo C, editors, Advances in Neural Networks - ISNN 2004: International Symposium on Neural Networks, Dalian, China, August 19-21, 2004, Proceedings, Part I. Berlin, Heidelberg: Springer . 2004. p. 406-412. (Lecture Notes in Computer Science). Epub 2004 Aug 16. doi: 10.1007/978-3-540-28647-9_68

A new neural network for nonlinear constrained optimization problems

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