A steepest descent method with a Wolf type line search

Abstract

The steepest decent method is proposed by French mathematician Cauchy and it is one of the simplest and oldest methods for solving unconstrained optimization problems. The steepest descent method, negative gradient direction is chosen as the search direction, also known as the gradient method. Usually, the step length \u03b1(cid:2921) of the steepest decent method can be computed by some inexact line search. In this paper, we will use a Wolfe type line search to evaluate the step length and its convergence property will be given under mild assumptions. From the numerical results, we can see that the steepest descent method with this Wolfe type line search is very promising. Finally, we give an application of the method to solve the nonlinear complementarity problem.