New line search methods for unconstrained optimization

It is well known that the search direction plays a main role in the line search method. In this paper, we propose a new search direction together with the Wolfe line search technique and one nonmonotone line search technique for solving unconstrained optimization problems. The given methods possess sufficiently descent property without carrying out any line search rule. The convergent results are established under suitable conditions. For numerical results, analysis of one probability shows that the new methods are more effective, robust, and stable, than other similar methods. Numerical results of two statistical problems also show that the presented methods are more interesting than other normal methods.