  Chordal decomposition techniques are used to reduce large structured positive
semidefinite matrix constraints in semidefinite programs (SDPs). The resulting
equivalent problem contains multiple smaller constraints on the nonzero blocks
(or cliques) of the original problem matrices. This usually leads to a
significant reduction in the overall solve time. A further reduction is
possible by remerging cliques with significant overlap. The degree of overlap
for which this is effective is dependent on the particular solution algorithm
and hardware to be employed. We propose a novel clique merging approach that
utilizes the clique graph to identify suitable merge candidates. We show its
performance by comparing it with two existing methods on selected problems from
a benchmark library. Our approach is implemented in the latest version of the
conic ADMM-solver COSMO.
