A mixed formulation for frictional contact problems prone to Newton like solution methods
Computer Methods in Applied Mechanics and Engineering
The regularization method for an obstacle problem
Numerische Mathematik
Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces
Nonlinear Analysis: Theory, Methods & Applications
Interior Methods for Nonlinear Optimization
SIAM Review
Semismooth Newton Methods for Operator Equations in Function Spaces
SIAM Journal on Optimization
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Interior Point Methods in Function Space
SIAM Journal on Control and Optimization
Path-following Methods for a Class of Constrained Minimization Problems in Function Space
SIAM Journal on Optimization
Uzawa block relaxation method for the unilateral contact problem
Journal of Computational and Applied Mathematics
Path-following for optimal control of stationary variational inequalities
Computational Optimization and Applications
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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.