Global Conference on Mathematics and Applications (GCMA)

The conjugate gradient (CG) method is known to be an efficient algorithm for large-scale unconstrained optimization owing to its low memory requirement and fast convergence properties. In this work, we propose a new hybrid nonlinear conjugate gradient method where the conjugate parameter \beta_k is defined as a convex combination of \beta_k^{NPRP} and \beta_k^{DY}. The combination parameter \theta_k is determined so as to satisfy the conjugacy condition. Under the strong Wolfe line search, we establish the sufficient descent property and prove the global convergence of the proposed method. Numerical experiments demonstrate that the new hybrid algorithm is both efficient and robust.