Chordal Decomposition

Clarabel implements a chordal decomposition and clique merging method to solve large-scale semidefinite programming problems. If the problem has favorable structure, this method can decompose a sparse positive semidefiniteness constraint on a large semidefinite cone into a collection of semidefinite constraints on a collection of smaller cones. This can lead to significant computational savings in terms of both memory and time.

Clarabel uses the same decomposition strategy as COSMO.jl. For details see our paper on clique merging techniques and this presentation by Michael Garstka.