Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization. Josz, C. & Molzahn, D. K. Submitted
Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization [pdf]Paper  Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization [link]Arxiv  abstract   bibtex   
We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming relaxations that grow tighter and tighter thanks to D'Angelo's and Putinar's Positivstellenstatz discovered in 2008. In other words, the Lasserre hierarchy may be transposed to complex numbers. We propose an algorithm for exploiting sparsity and apply the complex hierarchy to problems with several thousand complex variables. They consist in computing optimal power flows in the European high-voltage transmission network.
@article{josz_molzahn-complex_hierarchy,
	author={C. Josz and D. K. Molzahn},
	title={{Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization}},
	year={},
	note={Submitted},
	keywords={Polynomial Optimization,Optimal Power Flow},
	abstract={We consider the problem of finding the global optimum of a real-valued complex polynomial on a compact set defined by real-valued complex polynomial inequalities. It reduces to solving a sequence of complex semidefinite programming relaxations that grow tighter and tighter thanks to D'Angelo's and Putinar's Positivstellenstatz discovered in 2008. In other words, the Lasserre hierarchy may be transposed to complex numbers. We propose an algorithm for exploiting sparsity and apply the complex hierarchy to problems with several thousand complex variables. They consist in computing optimal power flows in the European high-voltage transmission network.},
	url_Paper={josz_molzahn-complex_hierarchy.pdf},
	url_arXiv={http://arxiv.org/abs/1508.02068},
}


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