Exploiting Sparsity in Complex Polynomial Optimization

2021/03/23 by Wang, Jie, Magron, Victor · 1 citation
#12D15 #14P10 #90C22 #90C23 #90C26 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2103.12444

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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• Sparse Polynomial Regression under Anomalous Data

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