NONMONOTONIC TRUST REGION ALGORITHM

A nonmonotonic trust region method for unconstrained optimization problems is presented. Although the method allows the sequence of values of the objective function to be nonmonotonic, convergence properties similar to those for the usual trust region method are proved under certain conditions, including conditions on the approximate solutions to the subproblem. To make the solution satisfy these conditions, an algorithm to solve the subproblem is also established. Finally, some numerical results are reported which show that the nonmonotonic trust region method is superior to the usual trust region method according to both the number of gradient evaluations and the number of function evaluations.