Research Of Constrained Programming Problems Based On Neural Dynamic Optimization

The constrained programming problems are important parts of the theories in systemsengineering, providing a lot of mathematical models for dealing with the practical modelingproblems, which play an indispensable role in applications such as industry, agriculture,commerce, management, military and other aspects in our life. The neural network is a kindof dynamic intelligent algorithm for real-time optimization calculation with fast convergencespeed and high efficiency. There are a variety of methods to build them. In view of quadraticprogramming problems and parametric programming problems, this paper mainly discuss themethods for building delayed projection neural networks and exact penalty function neuralnetworks. Moreover, some novel models are proposed and then their stability andconvergence are proved. Meanwhile, the specific calculation steps are given in detail.The main content and work of this thesis can be described briefly in the followingaspects:1. A class of delayed projection neural networks is studied. Taking into account thewidespread existence of delays, a type of delayed projection neural networks with delays inmore than one neuron is proposed to solve the quadratic programming problems. Based on theGronwall inequality and the Halanay inequality, it is strictly proved that the model is globallyexponential convergent. By comparing with the results of the existing literature, the researchshows that the present model is faster in convergence and of high efficiency.2. In consideration of solving the linear programming problems with parameters in bothobjective function and constraints, a new kind of neural networks based on L1exact penaltyfunction is proposed. The error function is firstly introduced to construct the approximatefunction of unit step function, which is used to give the smooth penalty function that moreaccurately approximates the L1exact penalty function. And then the dynamical equation ofneural networks is constructed by the gradient descent method. Moreover, the stability andconvergence of the proposed model are proved. Otherwise, the method is successfully appliedto solve the linear programming problems with parameters respectively in objective functionand the right-hand side vectors. By comparing with the results of the existing literature, theresearch shows that the present model is simple and of high precision.3. We discuss the exact penalty function neural networks which have some problems incurrent modeling process. Some existing methods are used for optimizations andimprovements to make the model precision and rational. The stability of the proposed modelis given. Furthermore, the method is successfully used to solve nonlinear programmingproblems with parameters in the right-side vectors of the inequality constraints. By comparingwith the results of the existing literature, the research shows that the present model hassmaller penalty factor and high accuracy.