A dwindling filter line search method for unconstrained optimization

In this paper, we propose a new dwindling multidimensional filter second-order line search method for solving large-scale unconstrained optimization problems. Usually, the multidimensional filter is constructed with a fixed envelope, which is a strict condition for the gradient vectors. A dwindling multidimensional filter technique, which is a modification and improvement of the original multidimensional filter, is presented. Under some reasonable assumptions, the new algorithm is globally convergent to a second-order critical point, when negative curvature direction is exploited. Preliminary numerical experiments on a set of CUTEr test problems indicate that the new algorithm is more competitive than the traditional second-order line search algorithms.