A trust region algorithm for nonsmooth optimization

A trust region algorithm is proposed for minimizing the nonsmooth composite function F(x)=h(f(x)), where f is smooth and h is convex. The algorithm employs a smoothing function, which is closely related to Fletcher’s exact differentiable penalty functions. Global and local convergence results are given, considering convergence to a strongly unique minimizer and to a minimizer satisfying second order sufficiency conditions.