Exploiting Sparsity in Complex Polynomial Optimization

Jie Wang; Victor Magron

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arXiv · 2103.12444

Exploiting Sparsity in Complex Polynomial Optimization

Jie Wang·Victor Magron

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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.

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Jie Wang, Victor Magron. 2021-03-23. Exploiting Sparsity in Complex Polynomial Optimization. https://arxiv.org/abs/2103.12444

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