Optimal CD-DY Conjugate Gradient Methods with Sufficient Descent

Conjugate Gradient (CG) methods are widely used for large scale unconstrained optimization problems. Most of CG-methods dont always generate a descent search direction, so the descent condition is usually assumed in the analysis and implementations. In this paper, we have studied several modified CG-methods based on the famous CD (CG-method), and show that our new proposed CG-methods produces sufficient descent and converges globally if the Wolfe conditions are satisfied. Moreover, they produces the original version of the CD (CG-method), if the line searches are exact. The numerical results show that the new methods are more effective and promising by comparing with the standard CD and DY (CG-methods).