NONMONOTONE TRUST REGION METHODS WITH CURVILINEAR PATH IN UNCONSTRAINED OPTIMIZATION

A general nonmonotone trust region method with curvilinear path for unconstrained optimization problem is presented. Although this method allows the sequence of the objective function values to be nonmonotone, convergence properties similar to those for the usual trust region methods with curvilinear path are proved under certain conditions. Some numerical results are reported which show the superiority of the nonmonotone trust region method with respect to the numbers of gradient evaluations and function evaluations.