  In this paper, we study the sparsity-adapted complex moment-Hermitian sum of
squares (moment-HSOS) hierarchy for complex polynomial optimization problems,
where the sparsity includes correlative sparsity and term sparsity. We compare
the strengths of the sparsity-adapted complex moment-HSOS hierarchy with the
sparsity-adapted real moment-SOS hierarchy on either randomly generated complex
polynomial optimization problems or the AC optimal power flow problem. The
results of numerical experiments show that the sparsity-adapted complex
moment-HSOS hierarchy provides a trade-off between the computational cost and
the quality of obtained bounds for large-scale complex polynomial optimization
problems.
