Solving Quadratic Programming Problems Based On Neural Networks

Optimization problems have been widely applied to scientific and engineering areas,such as signal and image processing, regression analysis and robot control, and so on.Artificial neural network, as a new subject, is considered to be a possible and verypromising approach to solve the optimization problems. Compared with traditionaloptimization algorithms, artificial neural network technique has more merits, such asfaster convergence rate, real-time control and hardware implementation, etc. In addition,due to the ubiquity of the time delay, it is necessary that the time delay is introduced intothe system in order to ensure the stability of the system. Therefore, the discussion of thedelayed project neural network for solving the optimization problems is of greattheoretical significance and practical value.In this thesis, by using saddle point theorem and projection theorem, we convert thequadratic programming problem into the problem of the projection equations. Based onthe projection equations and the delay theory, a delayed project neural network isconstructed, and the equilibrium point of network is equivalent to the optimal solution ofthe optimization problem. Then, the existence and uniqueness of the equilibrium point ofnetwork is proved based on saddle point theorem, and the global stability of the network isanalyzed. Finally, the simulations of several examples show the validity and thecorrectness of the network. Main content as follows:Firstly, we discuss a delayed project neural network for solving convex quadraticprogramming problems with linear constraints. By the variation-of-constants formula, theglobal exponential stability of the proposed neural network has been presented under someconditions.Secondly, we analysis a delayed project neural network for solving a class ofindefinite quadratic programming problems. By constructing a suitable Lyapunov-function,the global stability of the proposed neural network has been proved.Finally, we study a class of delayed project neural network for solving generalquadratic programming problems. By constructing a suitable Lyapunov-function and linear matrix inequality (LMI) methods, we get some sufficient conditions ensuring theglobal exponential stability of this network.