Open AccessSmoothing Neural Network for Non‐Lipschitz Optimization with Linear Inequality Constraints
Author(s) -
Xin YU,
Lingzhen WU,
Mian XIE,
Yanlin WANG,
Liuming XU,
Huixia LU,
Chenhua XU
Publication year - 2021
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2021.05.005
Subject(s) - lipschitz continuity , smoothing , artificial neural network , mathematical optimization , optimization problem , differential inclusion , mathematics , computer science , trajectory , point (geometry) , control theory (sociology) , mathematical analysis , artificial intelligence , control (management) , statistics , physics , geometry , astronomy
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.