# Semismooth newton and augmented lagrangian methods for a simplified friction problem

Research output: Contribution to journalArticle

### Abstract

In this paper a simplified friction problem and iterative second-order algorithms for its solution are analyzed in infinite dimensional function spaces. Motivated from the dual formulation, a primal-dual active set strategy and a semismooth Newton method for a regularized problem as well as an augmented Lagrangian method for the original problem are presented and their close relation is analyzed. Local as well as global convergence results are given. By means of numerical tests, we discuss among others convergence properties, the dependence on the mesh, and the role of the regularization and illustrate the efficiency of the proposed methodologies.

Original language English (US) 39-62 24 SIAM Journal on Optimization 15 1 https://doi.org/10.1137/S1052623403420833 Published - 2005

### Fingerprint

Augmented Lagrangian Method
Newton-Raphson method
Friction
Active Set Strategy
Semismooth Newton Method
A.s. Convergence
Infinite-dimensional Spaces
Primal-dual
Local Convergence
Global Convergence
Convergence Properties
Convergence Results
Function Space
Regularization
Mesh
Methodology
Formulation

### Keywords

• Augmented Lagrangians
• Friction problem
• Primaldual active set algorithm
• Semismooth Newton method

### ASJC Scopus subject areas

• Computer Science (miscellaneous)
• Mathematics(all)
• Analysis
• Applied Mathematics

### Cite this

In: SIAM Journal on Optimization, Vol. 15, No. 1, 2005, p. 39-62.

Research output: Contribution to journalArticle

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abstract = "In this paper a simplified friction problem and iterative second-order algorithms for its solution are analyzed in infinite dimensional function spaces. Motivated from the dual formulation, a primal-dual active set strategy and a semismooth Newton method for a regularized problem as well as an augmented Lagrangian method for the original problem are presented and their close relation is analyzed. Local as well as global convergence results are given. By means of numerical tests, we discuss among others convergence properties, the dependence on the mesh, and the role of the regularization and illustrate the efficiency of the proposed methodologies.",
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AB - In this paper a simplified friction problem and iterative second-order algorithms for its solution are analyzed in infinite dimensional function spaces. Motivated from the dual formulation, a primal-dual active set strategy and a semismooth Newton method for a regularized problem as well as an augmented Lagrangian method for the original problem are presented and their close relation is analyzed. Local as well as global convergence results are given. By means of numerical tests, we discuss among others convergence properties, the dependence on the mesh, and the role of the regularization and illustrate the efficiency of the proposed methodologies.

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