Research On Algorithm Of Several Optimization Problems

In this paper, several new steepest descent methods and nonlinear conjugate gradient methods are proposed to solve the unconstrained optimization problems. Under appropriate conditions, the global convergences of the methods are also given. And the numerical results showed that the proposed methods are effective.The first chapter of this paper studies the steepest descent method. We proposed a new steepest descent method with Wolfe type line search. And the convergence analysis and the numerical experiments are also given.The second chapter of this paper studies the nonlinear conjugate gradient methods.Under the condition of Wolfe type line search, the convergence analysis and the numerical results of the conjugate gradient method with the valued of objective function is proposed.In chapter three, we study the three-term conjugate gradient methods. Under certain conditions, the global convergence analysis of the method is presented and the related numerical experiments show the effectiveness of the method.A kind of the scaled conjugate gradient method is studied in the last chapter. The global convergence of the method is also given.