Chordal decomposition + barrier method + augmented Lagrangian algorithm for large scale buckling constraints

[mohamed82008]

Now that we have a differentiable assembly operator, we can use to do chordal decomposition by breaking down the large scale sparse SDP constraint into a bunch of small SDP constraints. We still need an equality constraint to specify that the relationship between the large scale sparse matrix K + c * Ksigma == assembleK(Ms) where Ms is the vector of small matrix decision variables of the same size as the element stiffness matrices, i.e. Ms[1] is of size ndofs_per_element x ndofs_per_element. With this formulation, we can then use SDPBarrierAlg of a PercivalAlg to solve the problem efficiently.

[samuelsonric]

@mohamed82008 is this still of interest? I have been working on a MathOptInterface layer to perform this decomposition.

[mohamed82008]

Yes it is of interest. I would be happy to give it a try.

[samuelsonric]

Thank you! Please let me know how it works :).

[samuelsonric]

Hi @mohamed82008! The package is now registered.