Can the non-linear conjugate gradient optimization method with Polak-Ribier line-search choice, be named as a quasi-Newton optimization technique?
If not, why?
A Newton based optimization method tries to find the roots of the gradient by Newton's method. This involves evaluating the Hessian and solving linear systems involving the Hessian. A quasi-Newton optimization technique use some approximation for the Hessian, or at least can be interpreted as implicitly using some approximation for the Hessian.
The non-linear conjugate gradient optimization method is not a quasi-Newton technique, because there is no Hessian involved, not even implicitly.