Veronika Karl, Frank Pörner
Published 2018-05-08Version 1
In this article we consider the semi-smooth Newton method for a class of variational inequalities. This class includes important problems like control constrained optimal control problems and state constrained optimal control problems in its penalized formulation. Moreover, Nash equilibrium problems are contained and the obstacle problem in its regularized dual formulation. We rewrite the variational inequality into a system of nonlinear equations and establish superlinear convergence for the associated Newton method. We also provide finite element discretizations for some important examples. Several numerical examples are presented to support the theoretical findings.
Optimistic Dual Extrapolation for Coherent Non-monotone Variational Inequalities
Sensitivity analysis of variational inequalities via twice epi-differentiability and proto-differentiability of the proximity operator
A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone
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