A generalized global convergence theory of projection-type neural networks for optimization

Rui Zhang; Zongben Xu

doi:10.1007/11596448_115

A generalized global convergence theory of projection-type neural networks for optimization

Rui Zhang
, Zongben Xu

School of Mathematics and Statistics

Xi'an Jiaotong University
Northwest University China

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

Abstract

The projection-type neural networks τdx/dt = -x + P_Ω(x - Λ(t)∂⁰E(x)) are generic and useful models for solving the constrained optimization problems min{E(x)|x ∈ amp; Ω}. In the existing convergence/stability analysis, the most are deduced based on the assumptions that E is uniformly or strictly convex and Ω is box-shaped. In this talk we present a generalized theory on convergence/stability of the networks. In the general setting that E is only convex and Ω is any closed bounded convex set, it is shown the global convergence/asymptotic stability of the networks in a specified sense. The presented theory sharpens and generalizes the existing results, and, consequently, underlies the applicability of the neural networks for a broader type of optimization problems.

Original language	English
Title of host publication	Computational Intelligence and Security - International Conference, CIS 2005, Proceedings
Publisher	Springer Verlag
Pages	777-784
Number of pages	8
ISBN (Print)	3540308180, 9783540308188
DOIs	https://doi.org/10.1007/11596448_115
State	Published - 2005
Event	International Conference on Computational Intelligence and Security, CIS 2005 - Xi'an, China Duration: 15 Dec 2005 → 19 Dec 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3801 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Conference on Computational Intelligence and Security, CIS 2005
Country/Territory	China
City	Xi'an
Period	15/12/05 → 19/12/05

Access to Document

10.1007/11596448_115

Cite this

Zhang, R., & Xu, Z. (2005). A generalized global convergence theory of projection-type neural networks for optimization. In Computational Intelligence and Security - International Conference, CIS 2005, Proceedings (pp. 777-784). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3801 LNAI). Springer Verlag. https://doi.org/10.1007/11596448_115

Zhang, Rui ; Xu, Zongben. / A generalized global convergence theory of projection-type neural networks for optimization. Computational Intelligence and Security - International Conference, CIS 2005, Proceedings. Springer Verlag, 2005. pp. 777-784 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A generalized global convergence theory of projection-type neural networks for optimization",

abstract = "The projection-type neural networks τdx/dt = -x + PΩ(x - Λ(t)∂0E(x)) are generic and useful models for solving the constrained optimization problems min\{E(x)|x ∈ amp; Ω\}. In the existing convergence/stability analysis, the most are deduced based on the assumptions that E is uniformly or strictly convex and Ω is box-shaped. In this talk we present a generalized theory on convergence/stability of the networks. In the general setting that E is only convex and Ω is any closed bounded convex set, it is shown the global convergence/asymptotic stability of the networks in a specified sense. The presented theory sharpens and generalizes the existing results, and, consequently, underlies the applicability of the neural networks for a broader type of optimization problems.",

author = "Rui Zhang and Zongben Xu",

year = "2005",

doi = "10.1007/11596448\_115",

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isbn = "3540308180",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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note = "International Conference on Computational Intelligence and Security, CIS 2005 ; Conference date: 15-12-2005 Through 19-12-2005",

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Zhang, R & Xu, Z 2005, A generalized global convergence theory of projection-type neural networks for optimization. in Computational Intelligence and Security - International Conference, CIS 2005, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3801 LNAI, Springer Verlag, pp. 777-784, International Conference on Computational Intelligence and Security, CIS 2005, Xi'an, China, 15/12/05. https://doi.org/10.1007/11596448_115

A generalized global convergence theory of projection-type neural networks for optimization. / Zhang, Rui; Xu, Zongben.
Computational Intelligence and Security - International Conference, CIS 2005, Proceedings. Springer Verlag, 2005. p. 777-784 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3801 LNAI).

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

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Zhang R, Xu Z. A generalized global convergence theory of projection-type neural networks for optimization. In Computational Intelligence and Security - International Conference, CIS 2005, Proceedings. Springer Verlag. 2005. p. 777-784. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11596448_115

A generalized global convergence theory of projection-type neural networks for optimization

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