Study On Nonlinear Conjugate Gradient Algorithms And Their Global Convergence

Conjugate gradient method is a classical method for solving unconstrained optimization problems.Researches on conjugate gradient method have been a lot of achievements.Based on the previous research,the following results are obtained:(1)Based on the DPRP and HCG conjugate gradient algorithms,we proposed a class of XW new conjugate gradient algorithm,which can guarantee the sufficient descent property without any line searches.This algorithm has an interesting property,namely the Property(*),and the global convergence property is established under the Wolfe line search.(2)Based on the WYL method and the DHS method,a hybrid nonlinear conjugate gradient method is proposed,which satisfies the sufficient descent property and the global convergence.(3)On the basis of FR method and MFR method,a kind of sufficient descent FR type conjugate gradient method is proposed.The global convergence of the method is proved under suitable conditions,and the numerical results are verified by numerical examples.(4)In this section,we construct a class of new nonlinear conjugate gradient method(XWH).The algorithm combines the DPRP method with the DHS method.The XWH method satisfies the property of descent,and its global convergence is obtained under the Wolfe line search.Numerical experiments show that the proposed method is more feasible and effective than the DPRP method and the DHS method.