1.Center for Research in Scientific Computation, Department of Mathematics,North Carolina State University,Raleigh,USA;2.Institut für Mathematik und Wissenschaftliches Rechnen,Universit?t Graz,Graz,Austria
Abstract:
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.