Applications of Semi-smooth Newton Methods to Variational Inequalities
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 control or state constraints, for example. The function F(x) for which we desire to find a root is typically Lipschitz continuous but not C 1 regular. The primal-dual active set strategy for the optimization with the inequality constraints is formulated as a semi-smooth Newton method. Sufficient conditions for global convergence assuming diagonal dominance are established. Globalization strategies are also discussed assuming that the merit function |F(x)|2 has appropriate descent directions.
KeywordsVariational Inequality Optimal Control Problem Global Convergence Descent Direction Merit Function
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