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Two Matrix-Type Projection Neural Networks for Solving Matrix-Valued Optimization Problems

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Neural Information Processing (ICONIP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11302))

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Abstract

In recent years, matrix-valued optimization algorithms have been studied to enhance the computational performance of vector-valued optimization algorithms. This paper presents two matrix-type projection neural networks, continuous-time and discrete-time models, for solving matrix-valued optimization problems. The proposed continuous-time neural network may be viewed as a significant extension to the vector-type double projection neural network. More importantly, the proposed discrete-time projection neural network can be parallelly implemented in terms of matrix state space. Under pseudo-monotonicity condition and Lipschitz continuous condition, it is guaranteed that the two proposed matrix-type projection neural networks are globally convergent to the optimal solution. Finally, computed examples show that the two proposed matrix-type projection neural networks are much superior to the vector-type projection neural network in computation speed.

This work is supported by the National Natural Science Foundation of China under Grant No. 61473330.

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Author information

Authors and Affiliations

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

    Lingmei Huang & Youshen Xia

  2. College of Mathematics and Computer Science, Wuyi University, Nanping, China

    Songchuan Zhang

Authors
  1. Lingmei Huang
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  2. Youshen Xia
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  3. Songchuan Zhang
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Corresponding author

Correspondence to Youshen Xia .

Editor information

Editors and Affiliations

  1. The Chinese Academy of Sciences, Beijing, China

    Long Cheng

  2. City University of Hong Kong, Kowloon, Hong Kong

    Andrew Chi Sing Leung

  3. Kobe University, Kobe, Japan

    Seiichi Ozawa

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Huang, L., Xia, Y., Zhang, S. (2018). Two Matrix-Type Projection Neural Networks for Solving Matrix-Valued Optimization Problems. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11302. Springer, Cham. https://doi.org/10.1007/978-3-030-04179-3_36

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  • DOI: https://doi.org/10.1007/978-3-030-04179-3_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04178-6

  • Online ISBN: 978-3-030-04179-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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