Some New Descent Nonlinear Conjugate Gradient Methods for Unconstrained Optimization Problems with Global Convergence

In this paper, we develop some three term nonlinear conjugate gradient methods based on the Hestenes-Stiefel (HS), the Polak-Ribiere-Polyak (PRP) and the Liu-Storey (LS) methods. The proposed algorithms always generate sufficient descent directions which satisfy g(k)(T) (d)k = -IIgkII(2). When the Wolfe or the Armijo line search is used, we establish the global convergence of the proposed methods in a concise way. Moreover, the linear convergence rate of the methods is discussed as well. The extensive numerical results show the efficiency of the proposed methods.