A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics
Numerical Analysis
2022-08-04 v1 Numerical Analysis
Abstract
We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric fourth-order tensor C. The projection problem is written as a semidefinite programming problem and an algorithm based on a primal-dual path-following interior point method coupled with a Mehrotra's predictor-corrector approach is proposed. Implementations based on direct methods are theoretically and numerically investigated taking into account tensors C arising in the modelling of masonry-like materials.
Keywords
Cite
@article{arxiv.2208.01947,
title = {A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics},
author = {Cristina Padovani and Margherita Porcelli},
journal= {arXiv preprint arXiv:2208.01947},
year = {2022}
}