Based On Recurrent Neural Network To Solve Nonsmooth And Nonconvex Optimization Problems

With the emergence of nonconvex optimization problems in Natural Science Engineering,the application of recurrent artificial neural networks to solve such optimization problems has become a hot topic.Artificial neural network has the ability of large-scale parallel processing,which can solve real-time problems and make up for the shortcomings of traditional methods to solve optimization problems.In recent decades,researchers have been devoted to the research of convex and nonconvex optimization problems,and put forward many neural networks to solve convex optimization problems.There are still some limitations in the research of nonconvex optimization problems.In order to enrich the neural networks to solve nonconvex optimization problems,based on the idea of differential inclusion,this paper constructs two different recurrent neural networks to solve nonsmooth and nonconvex optimization problems convex optimization problem.Firstly,in order to solve the nonsmooth and nonconvex optimization problems with inequality and equality constraints,a dynamic recurrent neural network based on the reaction force of objective function is constructed.Through rigorous analysis,the accuracy and effectiveness of the neural network are discussed.The solution of the neural network will converge to the optimal solution in a limited time,and the real and effective of the model is verified by simulation experiments.Compared with the existing neural networks,the model is simple in structure,and does not need to calculate complex penalty factors in advance,and the initial point of the neural network can be arbitrarily selected.Most importantly,the feasible region of the neural network does not need bounded constraints.Secondly,in order to solve a special kind of nonconvex optimization,that is problem pseudoconvex optimization problem,a dynamic recurrent neural network based on the reaction force of constraint function is constructed.In the same way,the accuracy of the neural network is also discussed rigorously in this paper.It is proved that the solution of the neural network enters into the feasible region in a limited time,and is finally stable in the optimal solution.The accuracy of the model is verified by two simulation experiments.The advantage of the neural network is that it does not need to calculate any precise penalty factor in advance,and the initial point can be chosen arbitrarily,the feasible region of inequality constraint can be unbounded,and the objective function can be unbounded in the feasible region of equality constraint.