Novel Neural Network for Dealing with a Kind of Non-smooth Pseudoconvex Optimization Problems

Abstract

Abstract: The research of optimization problem is favored by researchers.Nonsmooth pseudoconvex optimization problems are a special kind of nonconvex optimization problems,which often appear in machine learning,signal processing,bioinformatics and various scientific and engineering fields.Based on the idea of penalty function and differential inclusion,a new neural network me-thod is proposed to solve the non-smooth pseudoconvex optimization problems with inequality constraints and equality constraints.Under given assumptions,the solution of the RNN can enter in the feasible region in finite time and stay there there-after,at last converge to the optimal solution set of the optimization problem.Compared with other neural networks,the RNN has the following advantages:1)simple structure,it is a single-layer model;2)it is not need to compute an exact penalty parameter in advance;3)the initial point is chosed arbitrarily.Under the environment of MATLAB,mathematical simulation experiments show that state solution can converge to the optimal solution.At the same time,if the initial points are not selected properly,the state solution will not converge in limit time even can not converge.This not only verifies the effectiveness of the proposed RNN,but also shows that the proposed network has a wider range of applications.

Key words: Differential inclusion, Nonsmooth pseudoconvex optimization, Optimal solution set, Penalty parameter, Recurrent neural network(RNN)

CLC Number:

TP183

YU Xin, LIN Zhi-liang. Novel Neural Network for Dealing with a Kind of Non-smooth Pseudoconvex Optimization Problems[J].Computer Science, 2022, 49(5): 227-234.

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