A certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite-dimensional semismooth Newton methods, or in this case equivalently, primal-dual active set strategies. We present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem: first-order augmented Lagrangian, and path-following methods. The first strategy is based on a multiplier-update, while path-following with respect to the regularization parameter uses theoretical results about the path-value function to increase the regularization parameter appropriately. Comprehensive numerical tests investigate the performance of the proposed strategies for both a 2D as well as a 3D contact problem. © 2006 Elsevier B.V. All rights reserved.
Stadler, G. (2007). Path-following and augmented Lagrangian methods for contact problems in linear elasticity. Journal of Computational and Applied Mathematics, 203(2 SPEC. ISS.), 533–547. https://doi.org/10.1016/j.cam.2006.04.017