Abstract: Recently, Gilbert and Nocedal^[3] investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted β_K to non-negative value.[5] discussed the same problem as that in[3] and relaxed oh to be negative with the objective function being convex. This paper allows β_K to be selected in a wider range than[5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.

Key words: Polak-Ribière conjugate gradient method, strong Wolfe line search, global convergence