Exploiting Sparsity in Complex Polynomial Optimization

Jie Wang () and Victor Magron ()
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Jie Wang: Academy of Mathematics and Systems Science, CAS
Victor Magron: Laboratory for Analysis and Architecture of Systems, CNRS

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 1, No 14, 335-359

Abstract: 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.

Keywords: Complex moment-HSOS hierarchy; Correlative sparsity; Term sparsity; Complex polynomial optimization; Optimal power flow; 90C23; 14P10; 90C22; 90C26; 12D15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-021-01975-z

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