Application of a globally convergent hybrid conjugate gradient method in portfolio optimization

In this paper, we propose a modification that improves efficiency, robustness and reliability of the famous HS conjugate gradient method. In particular, we propose a hybrid of the HS and DHS methods, where DHS is another recent modification of the HS method. Irrespective of the line search, the search direction of the proposed method is sufficiently descent. Moreover, the new approach guarantees global convergence for general functions under the strong Wolfe line search. Numerical results and performance profiles are reported, and indicate that the new approach outperforms three similar methods in the literature. We also give a practical application of the new approach in minimizing risk in portfolio selection.