An efficient new hybrid CG-method as convex combination of DY and CD and HS algorithms

In this paper, we proposed a new hybrid conjugate gradient algorithm for solving unconstrained optimization problems as a convex combination of the Dai-Yuan algorithm, conjugate-descent algorithm, and Hestenes-Stiefel algorithm. This new algorithm is globally convergent and satisfies the sufficient descent condition by using the strong Wolfe conditions. The numerical results show that the proposed nonlinear hybrid conjugate gradient algorithm is efficient and robust.