Abstract: In this paper, a modified conjugate gradient formula beta _k^MLSbased on the formula of the Liu-Storey(LS) nonlinear conjugate gradient method was proposed. It was proved that under the Wolfe-Powell line search and even under the strong Wolfe-Powell line search, with parameter sigma in bigg(0,frac12bigg), the new method has sufficient descent and global convergence properties. Preliminary numerical results show that the method is very promising.

Key words: conjugate gradient method, SWP line search, global convergence, unconstrained optimization, conjugate gradient method, SWP line search, global convergence