Stability Of Neural Dynamical System Algorithms For Two Kinds Of Problems

There are nonlinear optimization problems in many fields such as scientific computation and engineering operation.Neural network algorithm is one of the effective algorithms to solve this problem.The neural dynamic algorithm has the distinct advantages of large scale parallel computing and fast convergence.In solving signal processing,image restoration,sparse optimization,etc.,it has the characteristics of strong operability and fast solution.Lyapunov stability theory and continuous-time dynamics algorithm are one of the important contents of accelerated optimization.Combined with the idea of neural network algorithm and continuous time optimization algorithm and accelerating algorithm optimization of ideas,this thesis studies the pseudo monotone variational inequality problems and the separation of convex feasible corresponding neural network algorithm of two types of problems,analyzed the corresponding algorithm of neural networks in finite time and the nature of the convergence of fixed time,can be applied to the signal recovery,the problem such as image processing.The main research work includes the following two aspects:In this thesis,an improved neural dynamic network(MNN)based on projection is proposed to solve the pseudo-monotone variational inequality.Under strong pseudo-monotonicity and Lipschitz continuity assumption,the MNN has a unique solution,and the relationship between the MNN and the corresponding neural dynamic network is obtained.In addition,the thesis establish the global fixed-time stability of MNN.The convergence time of MNN is independent of the initial conditions and uniformly bounded.Finally,a numerical example shows the feasibility and effectiveness of the proposed method.In this thesis,we propose a novel neural network which achieves stability within the fixed time(NFx NN)based on projection to solve the split convex feasibility problems.Under the bounded linear regularity assumption,the NFx NN admits a solution of the split convex feasibility problem.The thesis introduces the relationships between NFx NN and the corresponding neural networks.Additionally,the thesis also proves the fixed-time stability of the NFx NN.The convergence time of the NFx NN is independent of the initial states.The effectiveness and superiority of the NFx NN are also demonstrated by numerical experiments compared with the other methods.