A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics

Padovani C., Porcelli M.

Conic projection  Negative semidefinite tensors  Quadratic semidefinite programming  Interior point methods 

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 well-known symmetrization schemes and on direct methods are theoretically and numerically investigated taking into account tensors C arising in the modelling of masonry-like materials. For these special cases, indications on the preferable symmetrization scheme that take into account the conditioning of the arising linear systems are given.

Source: Calcolo (Online) 59 (2022). doi:10.1007/s10092-022-00478-1

Publisher: Springer Verlag Italia, Milano , Italia

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