Numerical behaviors of conjugate gradient methods with an Armijo type line search

In this paper, we consider several modified nonlinear conjugate gradient methods with an Armijo type line search proposed in [Y. D. Dong, A practical PR+ conjugate gradient method only using gradient, Appl. Math. Comput., 219 (2012) 2041-2052.]. Their numerical behaviors are investigated by utilizing a class of unconstrained nonlinear problems from the CUTEr test library and a class of boundary value problems. Numerical experiments for boundary value problems illustrate that the nonlinear conjugate gradient methods with the new line search can be directly applied to some problems whose original functions may be implicit while gradient information is available. And the comparisons of numerical performances among these methods illustrate that the hybrid versions are more efficient. © 2014 Binary Information Press.