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| Lagrange Neural Network for Nonsmooth Nonconvex Optimization Problems with Equality and Inequality Constrains |
| YU Xin① XU Zhijian① CHEN Zhaorong① XU Chenhua② |
①(School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China)
②(School of Electrical Engineering, Guangxi University, Nanning 530004, China) |
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Abstract Nonconvex nonsmooth optimization problems are related to many fields of science and engineering applications, which are research hotspots. For the lack of neural network based on early penalty function for nonsmooth optimization problems, a recurrent neural network model is proposed using Lagrange multiplier penalty function to solve the nonconvex nonsmooth optimization problems with equality and inequality constrains. Since the penalty factor in this network model is variable, without calculating initial penalty factor value, the network can still guarantee convergence to the optimal solution, which is more convenient for network computing. Compared with the traditional Lagrange method, the network model adds an equality constraint penalty term, which can improve the convergence ability of the network. Through the detailed analysis, it is proved that the trajectory of the network model can reach the feasible region in finite time and finally converge to the critical point set. In the end, numerical experiments are given to verify the effectiveness of the theoretic results.
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Received: 12 October 2016
Published: 18 May 2017
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| Fund: The National Natural Science Foundation of China (61462006, 51407037), The Natural Science Foundation of Guangxi Province (2014GXNSFAA118391) |
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Corresponding Authors:
XU Zhijian
E-mail: zhongxiawuyu@126.com
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