A nonmonotone trust region algorithm for unconstrained nonsmooth optimization

In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R~n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model which