Research Of Theory And Algorithm On Neural Network For Constrained Pseudoconvex Optimization

With the widespread emergence of generalized convex optimization problems in practical application, the method called neural network is applied to solve generalized convex optimization problems, which brings more and more attention. In recent decades, more and more mathematics workers have committed to the study of the convex, nonconvex optimization problems, constructed different neural network models, and proposed a series of solvable method to solve convex and nonconvex optimization problems. But there still exists limitations to solve generalized convex optimization problems. To improve existing results, deep study on the neural network for solving optimization problems holds theoretical significance and realistic value.In this paper, a neural network model with regularization item, which regards differential inclusion as model and holds good dynamic performances and optimal properties, is proposed for solving pseudoconvex optimization problems with general constraints. There are mainly three parts to illustrate efficiency of the neural network. Firstly, we employ penalty function method to deal with constrainted condition, and then we employ viscosity regularization method and the theory of diferential inclusions to proprose neural network with easier structure and better properties. In order to study dynamic behavior of the neural networks' solution further, we prove the local existence of the solution and employ Lyapunov energy function to prove the global existence, uniform boundedness and uniqueness of the solution. Secondly, we study the solution trajectory's dynamic behaviors and optimal properties of the neural network deeply. We prove the solution trajectory of neural network converges to feasible region according to the properties of Lyapunov energy function, and we conduct the solution trajectory of neural network is convergent and converges to a certain optimal solution of the optimal problem under some conditions.Finally, we prove the effectiveness of the proposed neural network to solve pseudoconvex optimization problems with general constraints by the numerical examples further.