Semismooth Newton and Augmented Lagrangian Methods for a Simplified Friction Problem

Georg Stadler (1)

1 Institut fur Mathematik

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.

Mots clés: friction problem; semismooth Newton method; augmented Lagrangians; primal-dual active set algorithm

Domaines: Sciences de l'ingénieur [physics]

Georg Stadler. Semismooth Newton and Augmented Lagrangian Methods for a Simplified Friction Problem. SIAM Journal on Optimization, 2004, 15 (1), pp.39-62. ⟨10.1137/S1052623403420833⟩. ⟨hal-01371364⟩