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

Abstract

Path-following splitting and semismooth Newton methods for solv- ing a class of problems related to elasto-plastic material deformations are pro- posed, 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 tech- nique and an associated lifting step yield local superlinear convergence in func- tion space. The lifting step accounts for the fact that the operator associated with the linear system in the Newton iteration need not be boundedly invert- ible (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.