A class of one parameter conjugate gradient methods

This paper proposes a class of one parameter conjugate gradient methods, which can be regarded as some kinds of convex combinations of some modified form of PRP and HS methods. The scalar βk   has the form of ϕkϕk−1μk. The convergence of the given methods is analyzed by some unified tools which show the global convergence of the proposed methods. Numerical experiments with the CUTE collections show that the proposed methods are promising.