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Solving Variational Inequality Problems with Linear Constraints Based on a Novel Recurrent Neural Network

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Advances in Neural Networks – ISNN 2007 (ISNN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4493))

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Abstract

Variational inequalities with linear inequality constraints are widely used in constrained optimization and engineering problems. By extending a new recurrent neural network [14], this paper presents a recurrent neural network for solving variational inequalities with general linear constraints in real time. The proposed neural network has one-layer projection structure and is amenable to parallel implementation. As a special case, the proposed neural network can include two existing recurrent neural networks for solving convex optimization problems and monotone variational inequality problems with box constraints, respectively. The proposed neural network is stable in the sense of Lyapunov and globally convergent to the solution under a monotone condition of the nonlinear mapping without the Lipschitz condition. Illustrative examples show that the proposed neural network is effective for solving this class of variational inequality problems.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, China

    Youshen Xia

  2. Department of Automation and Computer-Aided Engineering, The Chinese, University of Hong Kong, China

    Jun Wang

Authors
  1. Youshen Xia
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  2. Jun Wang
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Editor information

Derong Liu Shumin Fei Zengguang Hou Huaguang Zhang Changyin Sun

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Xia, Y., Wang, J. (2007). Solving Variational Inequality Problems with Linear Constraints Based on a Novel Recurrent Neural Network. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72395-0_13

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  • DOI: https://doi.org/10.1007/978-3-540-72395-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72394-3

  • Online ISBN: 978-3-540-72395-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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