A Class Of Conjugate Gradient Method

Optimization is a subject widely applied to discuss the best choice in decision-making and to seek the best solution. Finding algorithms with high performance in nonlinear optimization has been popular among researchers in optimization field. This thesis mainly deals with some new conjugate gradient methods for unconstrained optimization, which are based on Hestenes-Stiefel Algorithm. By adopting controlling or mixture measures, we make full use of the advantages of Hestenes-Stiefel Algorithm to put forward conjugate gradient methods related to Hestenes-Stiefel Algorithm and prove the global convergence of the algorithm. As a matter of fact, better numerical results are obtained with the new algorithm.In chapter 1, the development of optimization and some optimality conditions frequently used to determine the optimum solution are first introduced. Some sorts of derivative descent methods for nonrestraint programming are also reviewed.In chapter 2,by referring to the algorithm in paper[7],we present a class of conjugate gradient methods connected with Hestenes-Stiefel Algorithm. By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.In chapter 3,we presents a three terms hybrid conjugate gradient methods for unconstrained optimization based on Hestenes-Stiefel Algorithm and Dai-Yuan Algorithm,which had taken the advantages of two Algorithms. We proved it can ensure the convergence of the new methods under the Wolfe line search and without the descent condition. Additionally, our experimental results witness the applied value of this new method.