Path-following and augmented Lagrangian methods for contact problems in linear ...

• Author(s): Stadler, Georg
• Date: 2007
• Persistent ID: http://hdl.handle.net/10316/4604
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Contact problems; Path-following; Semismooth Newton methods; Active sets; Augmented Lagrangians; Primal-dual methods
• Document Type: Article
• Language: English

Description

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. http://www.sciencedirect.com/science/article/B6TYH-4K4PSP1-1/1/fde63c41201909b9bdb219e0a48dbc91