Applications of Semi-smooth Newton Methods to Variational Inequalities

摘要: This paper discusses semi-smooth Newton methods for solving nonlinear non-smooth equations in Banach spaces. Such investigations are motivated by complementarity problems, variational inequalities and optimal control problems with or state constraints, example. The function F(x) which we desire to find a root is typically Lipschitz continuous but not C1 regular. primal-dual active set strategy the optimization inequality constraints formulated as method. Sufficient conditions global convergence assuming diagonal dominance established. Globalization strategies also discussed that merit |F(x)|2 has appropriate descent directions.