A modified nonlinear conjugate gradient algorithm for unconstrained optimization and portfolio selection problems

Conjugate gradient methods play a vital role in finding solutions of large-scale optimization problems due to their simplicity to implement, low memory requirements and as well as their convergence properties. In this paper, we propose a new conjugate gradient method that has a direction satisfying the sufficient descent property.  We establish global convergence of the new method under the strong Wolfe line search conditions. Numerical results show that the new method  performs better than other relevant methods in the literature. Furthermore, we use the new method to solve a portfolio selection problem.