A Line Search Algorithm for Unconstrained Optimization

It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.