Smoothing Neural Network for Non-Lipschitz Optimization with Linear Inequality Constraints

YU Xin; WU Lingzhen; XIE Mian; WANG Yanlin; XU Liuming; LU Huixia; XU Chenhua

doi:10.1049/cje.2021.05.005

Volume 30 Issue 4

Jul. 2021

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Article Navigation > Chinese Journal of Electronics > 2021 > 30(4): 634-643

YU Xin, WU Lingzhen, XIE Mian, et al., “Smoothing Neural Network for Non-Lipschitz Optimization with Linear Inequality Constraints,” Chinese Journal of Electronics, vol. 30, no. 4, pp. 634-643, 2021, doi: 10.1049/cje.2021.05.005

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YU Xin, WU Lingzhen, XIE Mian, et al., “Smoothing Neural Network for Non-Lipschitz Optimization with Linear Inequality Constraints,” Chinese Journal of Electronics, vol. 30, no. 4, pp. 634-643, 2021, doi: 10.1049/cje.2021.05.005

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Smoothing Neural Network for Non-Lipschitz Optimization with Linear Inequality Constraints

doi: 10.1049/cje.2021.05.005

1. Department of Computer and Electronic Information, Guangxi University, Nanning 530004, China;
2. School of Computer Science and Engineering, Guilin University of Aerospace Technology, Guilin 541004, China;
3. The Guangxi Key Laboratory of Multimedia Communications and Network Technology, Nanning 530004, China;
4. Department of Electrical Engineering, Guangxi University, Nanning 530004, China

Funds:

This work is supported by the the Natural Science Foundation of China (No.61862004).

Received Date: 2017-08-26
Available Online: 2021-07-19
Publish Date: 2021-07-05

Abstract

Abstract

This paper presents a smoothing neural network to solve a class of non-Lipschitz optimization problem with linear inequality constraints. The proposed neural network is modelled with a differential inclusion equation, which introduces the smoothing approximate techniques. Under certain conditions, we prove that the trajectory of neural network reaches the feasible region in finite time and stays there thereafter, and that any accumulation point of the solution is a stationary point of the original optimization problem. Furthermore, if all stationary points of the optimization problem are isolated, then the trajectory converges to a stationary point of the optimization problem. Two typical numerical examples are given to verify the effectiveness of the proposed neural network.
- Non-Lipschitz optimization,
- Neural networks,
- Stationary points,
- Convergence

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