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This paper proposes a real moment-HSOS hierarchy for complex polynomial optimization problems with real coefficients. We show that this hierarchy provides the same sequence of lower bounds as the complex analogue, yet is much cheaper to solve. In addition, we prove that global optimality is achieved when the ranks of the moment matrix and certain s...
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... 15 with the 4th order relaxations of the three hierarchies. Related results are shown in Table 8. We make the following observations: (1) for n = 4, 5, 6, 7, R-HSOS, C-HSOS, and R-SOS provide the same lower bound; (2) for n ≥ 8, R-HSOS and C-HSOS provide the same lower bound while R-SOS runs out of memory; (3) R-HSOS is the fastest. ...Context 2
... 15 with the 4th order relaxations of the three hierarchies. Related results are shown in Table 8. We make the following observations: (1) for n = 4, 5, 6, 7, R-HSOS, C-HSOS, and R-SOS provide the same lower bound; (2) for n ≥ 8, R-HSOS and C-HSOS provide the same lower bound while R-SOS runs out of memory; (3) R-HSOS is the fastest. ...Similar publications
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