Exploiting Sparsity in Complex Polynomial Optimization
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2021
- DOI:
- 10.48550/arXiv.2103.12444
- arXiv:
- arXiv:2103.12444
- Bibcode:
- 2021arXiv210312444W
- Keywords:
-
- Mathematics - Optimization and Control
- E-Print:
- 20 pages, 6 tables