The Modified Conjugate Gradient Methods Based On BFGS

Conjugate gradient method is one of the effective method for solving unconstrained optimization problems.In recent years,many scholars study of conjugate gradient method,and obtained the good progress.At present,most literatures mainly study the conjugate parameters and conjugate direction of conjugate gradient method.By improving conjugate parameters and conjugate direction,many effective conjugate direction methods are obtained to solve unconstrained optimization problems.Based on BFGS method,four improved conjugate gradient methods are proposed in this paper.Firstly,the scaled quasi-Newton method with better performance than the traditional quasi-Newton method is combined with the symmetrical scaled Perry conjugate gradient method,which is improved on the Perry conjugate gradient method,and the conjugate parameters with better numerical effect are obtained by using the minimum distance method.At the same time,the search step size is accelerated,that is,the improved accelerated conjugate gradient method(XGACGSSV)based on memoryless BFGS is proposed.Secondly,the conjugate gradient method with constant parameters is improved,and the conjugate direction is approximated to the quasi-Newton direction with the minimum distance method to obtain the adaptive parameters,and the improved conjugate gradient method with better performance is obtained.This method has the advantages of quasi-newton method and conjugate gradient method,and is called the new conjugate gradient method(NCGSSV)based on memoryless BFGS.Thirdly,the memoryless BFGS method can reduce the storage space,and the conjugate gradient method has a fast convergence.Combining the advantages of the BFGS method and the conjugate gradient method,a new search direction is obtained by improving the search direction of conjugate gradient method.The improved PRP conjugate gradient method(MPRP)based on memoryless BFGS is obtained by improving the original PRP conjugate gradient method.Fourthly,the conjugate parameters in the Dai-Liao(DL)conjugate gradient method were improved,and the original conjugate parameters were changed to the adaptive conjugate parameters,to obtain an adaptive Dai-Liao conjugate gradient method that not only satisfies the descending and global convergence,but also has a good numerical experimental effect.