Delay Neural Network For Global Optimization Of Quadratic Programming

Mathematical programming problem of global optimization theory is an importantand difficult area of research. It is a nonlinear function of a region on the global optimalcharacteristics and methods of calculation. Since the objective function is usually notconvex function, specific regions are probably not convex; Therefore, global optimizationcan also be referred to as non-convex optimization. The need for global optimum solutionis not a condition that depicts a basic tool for the global optimal solution and sufficientcondition is portrayed a global optimum solution is a basic tool. This article discusses thesystem delay neural network model for quadratic programming, the establishment ofglobal optimality,existence of solutions,stability analysis and find the optimal solutionmethod.The first article discusses the sources of delay neural network model, detailedanalysis of the global optimization of research, gives the deterministic global optimizationalgorithm.Then studied with equality constraints and inequality constraints of the globaloptimum of quadratic programming, get the global exponential convergence of the system,Obtained a convergence point for the optimal solution of quadratic programming.Proved that when M is positive semi-definite matrix, delay neural network model onthe degradation of the global convergence of the optimal solution of quadraticoptimization, also verify that a stable point for the optimal solution.Finally, M is a generalized positive definite matrix for a new class of inequalityconstraints with indefinite quadratic programming problem; neural network model withdelay, system has been the existence of solutions and uniqueness. Application ofqualitative methods, construct an appropriate Lyapunov function, global convergence ofthe system has been optimized in the second sufficient condition for the optimal solution,and the matrix M is positive definite under the conditions of generalized, obtain theoptimal solution of the system.