Alternating direction method of multiplier for the unilateral contact problem with an automatic penalty parameter selection

Jonas Koko (1)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

We propose an alternating direction method of multiplier (ADMM) for the unilateral (frictionless) contact problem with an optimal parameter selection. We first introduce an auxiliary unknown to seprate the linear elasticity subproblem from the unilateral contact condition. Then an alternating direction is applied to the corresponding augmented Lagrangian. By eliminating the primal and auxiliary unknowns, at the discrete level, we derive a pure dual algorithm, starting point for the convergence analysis and the optimal parameter approximation. Numerical experiments are proposed to illustrate the efficiency of the proposed (optimal) penalty parameter selection method.

Mots clés: Linear elasticity; unilateral contact problem; alternating direction; augmented Lagrangian

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Jonas Koko. Alternating direction method of multiplier for the unilateral contact problem with an automatic penalty parameter selection. 2019. ⟨hal-02047516⟩