Research And Improvement Of The Optimization Method For Solving The Problem Of Nonlinear Equations

The idea of this paper is to transform the nonlinear equations into an unconstrained optimization problem.Then,used the optimization algorithms to solve constrained optimization problem.The main researches are as follows:We introduced the development status of memory gradient method,trust region algorithm,quasi-newton method,nonmonotone strategy and the main results obtained in this thesis.Desined three method for solving nonlinear equations.Firstly,presented a new non-monotone memory gradient algorithm for solving nonlinear equations.This algorithm is the combination of non-monotone line search technique and a modified memory gradient algorithm.Proved the global convergence.It's effective to solve the large scale problems.Otherwise,combined the modified nonmonotone step size rule with spare diagonal quasi-newton method.Designed a modified spare diagonal quasi-newton method for solving nonlinear equations.The global convergence properties of the new method are analyzed.The numerical results show that new method is effective.Lastly,presented a modified nonmonotone self-adaptive trust region algorithm for efficiently solving large scale nonlinear equations.This algorithm is the combination of trust region technique and modified quasi-newton equation.The global convergence properties of the new method are analyzed.The new method has stable convergence,so as to solve the large scale problems.Numerical examples show that the new method is effective.