We introduce a new method for solving a nonsmooth unconstrained optimization problem. This method is based on the solution of a variational problem and differs from other previously introduced methods in the following aspects: (a) a more sophisticated variational problem is now considered (b) the current trust region radius is computed in an automatic way. Preliminary computational results show that the new method performs quite well and can compete with other methods.

variational inequality, unconstrained optimization, nondifferentiable problems.