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A Discrete-Time Projection Neural Network for Solving Degenerate Convex Quadratic Optimization

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Abstract

This paper presents a discrete-time neural network to solve convex degenerate quadratic optimization problems. Under certain conditions, it is shown that the proposed neural network is stable in the sense of Lyapunov and globally convergent to an optimal solution. Compared with the existing continuous-time neural networks for degenerate quadratic optimization, the proposed neural network in this paper is more suitable for hardware implementation. Results of two experiments of this neural network are given to illustrate the effectiveness of the proposed neural network.

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Acknowledgments

This work was supported by Natural Science Foundation of China (Grant Nos. 61403313, 61374078), Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2015jcyjBX0052) and also supported by the Natural Science Foundation Project of Chongqing CSTC (No. cstc2014jcyjA40014). This publication was made possible by NPRP Grant No. NPRP 4-1162-1-181 from the Qatar National Research Fund (a member of Qatar Foundation).

Author information

Authors and Affiliations

  1. School of Electronics and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Zican Zhang, Chuandong Li & Xing He

  2. Department of Mathematics, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

    Tingwen Huang

Authors
  1. Zican Zhang
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  2. Chuandong Li
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  3. Xing He
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  4. Tingwen Huang
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Corresponding author

Correspondence to Chuandong Li.

Appendix

Appendix

Proof of Theorem 1

First, we can construct a Lyapunov function

where is one equilibrium point. Then calculating the difference

(21)

and then, by simple calculation,

Using the inequality in Lemma 1, it follows that

(22)

While

is a semi-positive definite matrix.

Therefore, if the constant satisfies

(23)

That is

(24)

We obtain

(25)

therefore, the network (16) we present is globally convergent. This proof is complete. \(\square \)

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Zhang, Z., Li, C., He, X. et al. A Discrete-Time Projection Neural Network for Solving Degenerate Convex Quadratic Optimization. Circuits Syst Signal Process 36, 389–403 (2017). https://doi.org/10.1007/s00034-016-0308-5

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