The paper starts with a concise description of the recently developed semismooth* Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one obtains an implementable algorithm exhibiting a local superlinear convergence. Thereafter we suggest several globally convergent hybrid algorithms in which one combines the semismooth* Newton method with selected splitting algorithms for the solution of monotone variational inequalities. Their efficiency is documented by extensive numerical experiments.
@article{arxiv.2007.11420,
title = {On the application of the semismooth* Newton method to variational inequalities of the second kind},
author = {Helmut Gfrerer and Jiri V. Outrata and Jan Valdman},
journal= {arXiv preprint arXiv:2007.11420},
year = {2020}
}