Research On Quadratic Convergence Of Two Kinds Of Nonlinear Conjugate Gradient Methods

Conjugate gradient method is one of the main methods for solving unconstrained optimization problems. Because of simple and convenient storage, etc, it is very suitable for solving the large-scale unconstrained optimization problems. The convergence of method plays an important role in measure of the effectiveness. In this paper, we mainly study quadratic convergence on two kinds of modified conjugate gradient methods.In the first chapter, we simply introduce the general structures of the optimization problems. At the same time, the main achievements in the field of conjugate gradient methods are reviewed.In the second chapter, we mainly review some basic knowledge about the optimizations, which is usually used in this paper. On the basis of above conten-ts, we have made the detailed discussion about the quadratic convergence of two kinds of methods.The third chapter mainly presents a new modified MPRP*method, which called the MPRP*method. We show that the MPRP*method with Armijo line search is linear convergence. We introduce a way of choosing the initial step with Armijo line search and Wolfe line search. We also prove that the MPRP*method with a restart strategy still retains n-step quadratic convergence under the suitable assumptions. Numerical experimental results show that the MPRP*method using restart is superior to the method which didn’t use the restart technology.In the fourth chapter, we simply review the WYL method. On the basis of chapter3, we increase the appropriate assumptions. We also showed that the WYL method with a restart strategy still retains n-step quadratic convergence under the new assumptions conditions. Numerical experimental results also show that the WYL method using restart is superior to the method which didn’t use the restart strategy.