A New Conjugate Gradient Method with Sufficient Descent without any Line Search for Unconstrained Optimization

Conjugate gradient methods are one of the most used methods for solving nonlinear unconstrained optimization problems, especially of large scale. Their wide applications are due to their simplicity and low memory requirement. The sufficient descent property is an important issue in the analyses and implementations of conjugate gradient methods. In this paper, a new conjugate gradient method is proposed for unconstrained optimization problems. The theoretical analysis shows that the directions generated by the new method are always satisfy the sufficient descent property, and this property is independent of the line search used. Furthermore, a numerical experiment based on comparing the new method with other known conjugate gradient methods shows that the new is efficient for some unconstrained optimization problems.