A New Modified HS Conjugate Gradient Method and the Global Convergence

In this paper, we propose a new modified HS conjugate gradient method for unconstrained optimization. An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective function. This property is independent of the line search used. In particular, exact line search is used, the method reduces to the standard HS conjugate gradient method. Under appropriate conditions, we show that the new modified HS conjugate gradient method with Wolfe line search is globally convergent. Numerical experiments show that the proposed algorithm is effective.