A new efficient conjugate gradient method for unconstrained optimization

We propose a nonlinear conjugate gradient method for unconstrained optimization based on solving a new optimization problem. Our optimization problem combines the good features of the linear conjugate gradient method using some penalty parameters. We show that the new method is a subclass of Dai–Liao family, the fact that enables us to analyze the family, closely. As a consequence, we obtain an optimal bound for Dai–Liao parameter. The global convergence of the new method is investigated under mild assumptions. Numerical results show that the new method is efficient and robust, and outperforms CG-DESCENT.