Curvilinear paths and trust region methods with nonmonotonic back tracking technique for unconstrained optimization (Q2732177)

The main purpose of this paper is to modify a type of approximate trust region methods via two curvilinear paths for unconstrained optimization. A mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region sub-problem is unacceptable.NEWLINENEWLINENEWLINEMain result: A series of properties of both optimal path and modified gradient path are presented. The global convergence or the fast local convergence rate of the proposed algorithms are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases.