Conjugate Gradient Methods for Nonconvex Problems

It is worthwhile to notice that when interests in conjugate gradient algorithms for quadratic problems subsided their versions for nonconvex differentiable problems were proposed. These propositions relied on the simplicity of their counterparts for quadratic problems. As we have shown in the previous chapter a conjugate gradient algorithm is an iterative process which requires at each iteration the current gradient and the previous direction. The simple scheme for calculating the current direction was easy to extend to a nonquadratic problem

$${\rm min}_{_{_{{\!\!\!\!\!\!\!\!\!\!\!\!\!\!x\in R^n}}}}f(x)$$

((2.1))

.