The global convergence of the Polak–Ribière–Polyak conjugate gradient algorithm under inexact line search for nonconvex functions

Powell (1984) and Dai (2003) constructed respectively a counterexample to show that the Polak–Ribière–Polyak (PRP) conjugate gradient algorithm fails to globally converge for nonconvex functions even when the exact line search technique is used, which implies similar failure of the weak Wolfe–Powell (WWP) inexact line search technique. Does another inexact line search technique exist that can ensure global convergence for nonconvex functions?...