I. Introduction
Let be an n-dimensional Euclidean space and is a continuously differentiable function. Unconstrained minimization problem (UP) is to find the minimal point of over , denoted by\min f(x),\quad x\in R^{n}.
Most of the well-known methods for solving (UP) take the formx_{k+1}=x_{k}+\alpha_{k}d_{k}, k=1,2, \ldots,
\eqno\hbox{(1)}
where is a search direction of at and is a positive step-size. If is the current point, we denote by by and by , respectively.