On a semi-smooth Newton method and its globalization

Abstract

This paper addresses the globalization of the semi-smooth Newton method for non-smooth equations F(x) = 0 in $${\mathbb{R}}^m$$ 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.