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.