Two nonmonotone trust region algorithms based on an improved Newton method

Abstract

In this paper, we present two improved regularized Newton methods for minimizing nonconvex functions with the trust region method. The fundamental idea of this method is based on the combination of nonmonotone Armijo-type line search proposed by Gu and Mo (Comput Math Appl 55:2158–2172, 2008) and the traditional trust region method. Under some standard assumptions, we analyze the global convergence property for the new methods. Primary numerical results are reported. The obtained results confirm the higher efficiency of the modified algorithms compared to the other presented algorithms.