Several Classes Of Sufficient Descent Conjugate Gradient Methods

The nonlinear conjugate gradient method is an important method for solving large-scale unconstrained optimization problems.It has the advantages of less information storage,simple algorithm and easy programming.In recent years,with the rapid development of computers and the emergence of large-scale optimization problems,the research of conjugate gradient method is focused on seeking efficient and fast method.In this paper,several different conjugate gradient methods are proposed on the basis of previous studies on conjugate gradient methods,and their descent and con-vergence are studied.Through a series of numerical experiments,their effectiveness is proved.The results obtained are as follows:1.The second chapter the discusses and studies the classical conjugate gradient method,a new parameter variable^*₆)is proposed,based on which a new conjugate gradient method is constructed.When the step size factor₆)is applied to the stan-dard Wolfe-Powell line search condition,it is proved that the new conjugate gradient method has sufficient descent and global convergence.Finally,the effectiveness of the algorithm is verified by numerical experiments.2.In the research of commonly used inexact line search,a modified weak Wolfe-Powell line search,called MWWP line search,is proposed in reference[63]under the BFGS algorithm.In the third chapter,two different conjugate gradient methods are constructed based on the MWWP line search conditions,which are combined with the classical Dai-Yuan conjugate gradient method and the new conjugate gradient method proposed in the second chapter.It has been proved that both of the two methods satisfy sufficient descent and global convergence under the MWWP line search condition,and the effectiveness of the two algorithms is further verified by the corresponding numerical experiments.