Abstract: The research of optimization problem is favored by researchers.As an important part of optimization pro-blem,convex optimization problem is the focus of research.Many models based on neural network are applied to practical problems.However,the optimization problems involved in machine learning,signal processing,bioinformatics and other fields are often not convex optimization problems,but pseudoconvex optimization and nonconvex optimization problems.Therefore,it is urgent to solve the latter kind of problems.To solve the optimization problem that the objective function is nonsmooth pseudoconvex function and constraint function is equality and inequality function,this paper constructeda new single-layer neural network model without penalty parameter based on the idea of penalty function and differential inclusion.The main idea of the design is that according to the proposed neural network model,a constrained function can be designed for the gradient of the objective function so that the value of the objective function is always kept within a range,and then a function about time is combined to ensure that its value decreases with time.At the same time,considering that inequality constraints affect the convergence direction of the state solution before it enters the equation constraint,a conditional function is added to restrict it.Compared with the proposed neural network model,it has the advantages of simple structure,no need to calculate penalty parameters in advance,and no special requirements for the position of the initial point.Furthermore,it is theoretically proved that for any initial point,the state solution can converge to the equality constraints in finite time and stay there thereafter,the boundedness of the state solution,the state solution can converge to the feasible region in finite time and stay there thereafter,and the state solution can finally converge to the optimal solution of the optimization problem.Under the environment of MATLAB,by mathematical simulation experiments,the state solution can converge to the optimal solution quickly.At the same time,if the penalty parameters or initial points are not selected properly,the state solution will not converge well when the same optimization problem is solved by using the proposed similar neural network model.This not only verifies the correctness of the theoretical results,but also shows that the proposed network has a wider range of applications.

Key words: Differential inclusion, Neural network, Nonsmooth optimization, Pseudoconvex function