Several path-following methods for a class of gradient constrained variational inequalities

Abstract

Path-following splitting and semismooth Newton methods for solving a class of problems related to elasto-plastic material deformations are proposed, analyzed and tested numerically. While the splitting techniques result in alternating minimization schemes, which are typically linearly convergent, the proposed Moreau–Yosida regularization based semismooth Newton technique and an associated lifting step yield local superlinear convergence in function space. The lifting step accounts for the fact that the operator associated with the linear system in the Newton iteration need not be boundedly invertible (uniformly along the iterates). For devising an efficient update strategy for the path-following parameter regularity properties of the path are studied and utilized within an inexact path-following scheme for all approaches. The paper ends by a report on numerical tests of the different approaches.