Research On Transient Chaotic Neural Network For Nonsmooth And Nonconvex Optimization

As an important problem of science and engineering application,optimization problem has always been a research hotspot in the field of science and technology.The corresponding solutions are also becoming more and more diverse,among which neural network has become one of the most important solutions for optimization problems by virtue of its strong autonomous learning ability,high-speed parallel computing,big data processing and other advantages.After a great breakthrough in convex optimization problem,People will focus on nonconvex optimization problems.However,the traditional recurrent neural network based on gradient descent mechanism is easy to stay in the local minimum value.In order to solve this problem,this paper proposes effective solution based on the idea of neural network.Firstly,based on the idea of penalty function,a class of single-layer neural networks without Lipschitz constant calculation is designed,and a new recurrent neural network model is proposed to solve a class of nonsmooth and nonconvex optimization problem with constraints.Then it is proved that the global solution of the recurrent neural network exists under the condition that the feasible region is bounded,and that the state variables can enter and stay in the feasible region in finite time,and finally converge to a critical point of the optimization problem.Finally,the effectiveness of the proposed method is verified by simulation experiments and constructing a single observation non convex and nonsmooth sparse reconstruction model in the field of compressed sensing.Then,on the basis of recurrent neural network model,two kinds of transient chaotic neural network models are extended.The chaotic ergodic property of transient chaotic mechanism,the random walk property of noise mechanism and the simulation neuron property of simulating biological mechanism are used to ensure that the network state solution can converge to the global optimal solution of the optimization problem.Then,the parameters of the transient chaotic neural network model are analyzed,and the corresponding physical meaning is explained.Combined with the actual test,the appropriate value range of each parameter is given.Finally,the convergence and global optimization ability of the transient chaotic neural network are verified by numerical experiments.