Strengthening Lasserre's Hierarchy in Real and Complex Polynomial Optimization
arxiv(2024)
摘要
We establish a connection between multiplication operators and shift
operators. Moreover, we derive positive semidefinite conditions of finite rank
moment sequences and use these conditions to strengthen Lasserre's hierarchy
for real and complex polynomial optimization. Integration of the strengthening
technique with sparsity is considered. Extensive numerical experiments show
that our strengthening technique can significantly improve the bound
(especially for complex polynomial optimization) and allows to achieve global
optimality at lower relaxation orders, thus providing substantial computational
savings.
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