The R-convergence rate of MDY conjugate gradient method with inexact line search for unconstrained optimization

It is well-known that the Dai-Yuan conjugate gradient method. Recently, Zhang developed two modified Dai-Yuan (MDY) methods that are globally convergence if the standard Armijo line search is used. In this paper, firstly, we investigate the R-convergence rate of the MDY method with inexact Armijo line search. Secondly, We show another MVDY method convergence globally for nonconvex minimization problems. Thirdly, the MVDY method also have R-convergence rate with inexact Armijo line search. Numerical results show that this algorithm is effective in unconstrained optimization problems.