Projection Neural Networks With Time Delay For Quadratic Programming

Generation and development of artificial neural network, and can be used to solvemany optimization problems in mathematical programming, neural network hardwareimplementation, the neurons in the neural network in information will appear in the circuitimplementation of real time delay, this phenomenon will lead to oscillation phenomenonand the instability phenomenon in a neural network, so the research time delay neuralnetworks with time delay both in theory and practice has positive significance, due to thedelay of universality, time-delay, introduced in the system, not only can ensure thestability of the system, but also very good, we have acquired the proof of the stability, hasimportant theoretical and application value.Paper using the basic theory of optimization of the saddle point theorem andprojection theorem projection equations will be converted into a quadratic programmingproblem to solve the problem of recycling projection equation and theory of delay delayprojection neural network is constructed, the network equilibrium is the optimal solutionof quadratic programming problem. The main contents are as follows:Firstly, studying a class of inequality constrained quadratic programming problem,Lagrangian coefficients were used to obtain new models and constructing an appropriateLyapunov function method, obtain the dual problem, obtained by substituting the optimalsolution of the initial problem and global stability that the new model.Secondly, studying projected a new delay neural network model to solve quadraticprogramming problems, the use of functional differential equations, construct appropriateLyapunov function, the system is given sufficient conditions for global asymptoticstability.Finally, by using Lagrange multipliers, the use of functional differential equationstheory and scaling methods, proved that the new model of existence and uniqueness ofsolutions, and gives projective lag neural networks sufficient conditions for globalexponential stability. Used to solve optimization problems in a series of constraintsquadratic programming problem.