On The Memory Gradient Method And Its Applications In Solving The System Of Nonlinear Equation

In this dissertation, we mainly investigated the convergence of memory gradient methods for unconstrained optimization problems. We also apply memory gradient methods in solving system of nonlinear equations. At first, we reformulate nonlinear equations into an unconstrained optimization problem and then we design a new memory gradient method. The dissertation has three chapters.Chapter 1 is the introduction. We described the research situations of memory-gradient method and nonlinear equations. The main contributions are also stated briefly.In Chapter 2, we proposed a new memory gradient method for unconstrained optimization problems and proved the global convergence when using curve search rule in the algorithm. Comparing with other memory gradient methods, the superiority of this method is that the global convergence is guaranteed. The new method has numerical stable property due to using previous iterative information to produce next iterate.In chaper 3, we presented a new memory gradient method for nonlinear equations. At first, we reformulated nonlinear equations into an unconstrained optimizition problem and then designed a memory-gradient method. In the algorithm, we don't need to compute and memorize Jacobi matrix. As a result, the amount of computation and storage is saved in practical computation. Numerical results showed that this memory gradient method is feasible and efficient.