A New Class Of Conjugate Gradient Algorithm

With its rapid development,optimization is used on a large scale by us nowadays. Especially,finding high performance algorithms in nonlinear optimization is a very heated research topic for the optimization specialists. Many algorithms were developed in recent years ,among these axe conjugate gredient method , quasi-Newton method , and so on.And people try to prove the convergence of the methods. This paper presents some new conjugate gradient methods for unconstrained optimization,which are based on Polak-Ribiere Algorithm and Fletcher-Reeves Algorithm.As a attempt,we get to use both of the advantages of Polak-Ribiere Algorithm and Fletcher-Reeves Algorithm synthetically. Simultaneously,we prove that the Grippo line search condition can ensure the global convergence. Finally,we also get better numerical results with the new algorithm.In chapter 1 ,we introduce the development of optimization and some extensive optimality conditions to determine the optimum solution. Then we review several extensive derivative descent methods for unconstrained programming .In chapter 2,we improve the algorithm in paper [1] and prove the global convergence of the algorithm wih realizable Grippo line search and weaker preconditions but not the theoretic exact line search and the twice continuously differentiable condition on bounded sets of cost function in paper [1] . Moreover,we find that the subsequent experimental performance are more efficient than that of traditional algorithms.In chapter 3,we propose a new class of conjugate gradient method with inexact Grippo line search for unconstrained nonlinear programming problems by combining Polak-Ribiere Algorithm with Fletcher-Reeves Algorithm via adjustable parameter.This algorithm has a special form of radical sign.It's global convergence is proved under suitable conditions. Additionally, our experimental results witness the applied value of this new method.