A conjugate gradient method with sufficient descent property

In this paper, a new nonlinear conjugate gradient method is proposed, whose search direction can be viewed as a simple approximation to that of the memoryless BFGS method. The search direction of the proposed method satisfies the sufficient descent property regardless of line search. Global convergence properties of the new method are explored on uniformly convex functions and general functions with the standard Wolfe line search. Numerical experiments are done to test the efficiency of the new method, which implies the new method is promising.