Conjugate Gradient Methods With Non-monotone Rule And Its Convergence

In this paper,the main content of the thesis is presented as follows:In Chapter 2,based on the RMFI conjugate gradient method and the Zhang H.C.non-monotone strategy,a new kind of conjugate gradient method for solving large scale unconstrained optimization problems is presented.Under mild conditions,the presented method with the Zhang H.C.rule converges globally.Numerical results show that the new method is more efficient by compared with RMFI method with Zhang H.C.rule.In addition,we extend Zhang H.C.non-monotone line search technique by forcing function,and theoretically,we have proved the new conjugate gradient method's global convergence with the extended model.In Chapter 3 and Chapter 4,we still modify the RMFI formula,and the new ?k can ensure each step of the iterative direction descends fully.We also prove that the proposed methods converge globally with Zhang H.C.non-monotone rule under some reasonable conditions.Lastly,Numerical results show that the new algorithms are efficient.In Chapter 5,based on the RMIL method and Zhang H.C.non-monotone rule,a new kind of conjugate gradient method for solving large scale unconstrained optimization is proposed.We also prove that the proposed method converges globally under certain conditions.Some numerical examples are employed to illustrate the effectiveness of our proposed method.