On a semi-smooth Newton method and its globalization

This paper addresses the globalization of the semi-smooth Newton method for non-smooth equations F(x)  =  0 in with applications to complementarity and discretized ℓ¹-regularization problems. Assuming semi-smoothness it is shown that super-linearly convergent Newton methods can be globalized, if appropriate descent directions are used for the merit function |F(x)|². Special attention is paid to directions obtained from the primal-dual active set strategy. K. Ito’s research was partially supported by the Army Research Office under DAAD19-02-1-039.