Globally convergent conjugate gradient algorithms without the Lipschitz condition for nonconvex optimization

It is well known that under the Wolfe–Powell inexact line search, global convergence of nonlinear conjugate gradient method always requires Lipschitz continuous condition for nonconvex functions. In this paper, we find unnecessary proving particular algorithms if its searching direction has well-known sufficient descent property and trust region feature. Thus, family proposed by Yuan et al. (Numer. Algorithms, 84(2020)) established without functions since they have these two properties. Furthermore, a new algorithm search technique presented, also analysed suitable assumptions. The numerical results show performance competitive with some problems.