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The classical trust region algorithm was extended to the nonsmooth minimization problem successful by Qi and Sun. Combining the trust region algorithm of Qi and Sun with the nonmonotone technique, this paper present a nonmonotone trust region algorithm for the unconstrained nonsmooth optimization problems where the objective function is locally Lipschitzian, the local convergence results are established.

In this survey paper we present an overview of derivative-free optimization, including basic concepts, theories, derivative-free methods and some applications. To date, there are mainly three classes of derivative-free methods and we concentrate on two of them, they are direct search methods and model-based methods. In this paper, we first focus on unconstrained optimization problems and review some classical direct search methods and model-based methods in turn for these problems. Then, we survey a number of derivativefree approaches for problems with constraints, including an algorithm we proposed for spherical optimization recently.

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