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Global exponential stability of a neural network for inverse variational inequalities

Global exponential stability of a neural network for inverse variational inequalities
Global exponential stability of a neural network for inverse variational inequalities

We investigate the convergence properties of a projected neural network for solving inverse variational inequalities. Under standard assumptions, we establish the exponential stability of the proposed neural network. A discrete version of the proposed neural network is considered, leading to a new projection method for solving inverse variational inequalities, for which we obtain the linear convergence. We illustrate the effectiveness of the proposed neural network and its explicit discretization by considering applications in the road pricing problem arising in transportation science. The results obtained in this paper provide a positive answer to a recent open question and improve several recent results in the literature.

Dynamic programming, Exponential stability, Neural network, Road pricing problem, Variational inequality
0022-3239
915-930
Vuong, P.T
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
He, Xiaozheng
aaee9be2-028c-4b77-a2e6-df8ec6c8778c
Viet Thong, Duong
77732f91-02df-46ab-b394-b87518ec4e68
Vuong, P.T
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
He, Xiaozheng
aaee9be2-028c-4b77-a2e6-df8ec6c8778c
Viet Thong, Duong
77732f91-02df-46ab-b394-b87518ec4e68

Vuong, P.T, He, Xiaozheng and Viet Thong, Duong (2021) Global exponential stability of a neural network for inverse variational inequalities. Journal of Optimization Theory and Applications, 190 (3), 915-930. (doi:10.1007/s10957-021-01915-x).

Record type: Article

Abstract

We investigate the convergence properties of a projected neural network for solving inverse variational inequalities. Under standard assumptions, we establish the exponential stability of the proposed neural network. A discrete version of the proposed neural network is considered, leading to a new projection method for solving inverse variational inequalities, for which we obtain the linear convergence. We illustrate the effectiveness of the proposed neural network and its explicit discretization by considering applications in the road pricing problem arising in transportation science. The results obtained in this paper provide a positive answer to a recent open question and improve several recent results in the literature.

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More information

Accepted/In Press date: 4 August 2021
e-pub ahead of print date: 4 August 2021
Published date: 4 August 2021
Additional Information: Funding Information: The authors are very thankful to both anonymous referees for their careful reading and constructive comments, which helped to improve the presentation of the paper. This work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) project 101.01-2019.320. The second author acknowledges the support of the U.S. National Science Foundation under Grant CMMI-2047793. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords: Dynamic programming, Exponential stability, Neural network, Road pricing problem, Variational inequality

Identifiers

Local EPrints ID: 450952
URI: http://eprints.soton.ac.uk/id/eprint/450952
ISSN: 0022-3239
PURE UUID: aa8207df-ad08-4870-bccf-fbbc580db164
ORCID for P.T Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 26 Aug 2021 16:30
Last modified: 26 Nov 2021 03:20

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Contributors

Author: P.T Vuong ORCID iD
Author: Xiaozheng He
Author: Duong Viet Thong

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