A quasi-Newton method for unconstrained non-smooth problems

We present a method, based on a variational problem, for solving a non-smooth unconstrained optimization problem. We assume that the objective function is a Lipschitz continuous and a regular function. In this case the function of our variational problem is semismooth and a quasi-Newton method may be used to solve the variational problem. A convergence theorem for our algorithm and its discrete version is also proved. Preliminary computational results show that the method performs quite well and can compete with other methods.