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Center for Nonlinear Studies |
Multivariate polynomial optimization where variables and data are complex numbers is a non-deterministic polynomial-time hard problem that arises in various applications such as electric power systems, imaging science, signal processing, and quantum mechanics. To address these problems, we transpose to complex numbers the Lasserre hierarchy, which aims to solve real polynomial optimization problems to global optimality. We use it to solve the optimal power flow on large sections of the European high-voltage electricity transmission network. (We contributed the test cases to the research community while working with French Transmission System Operator.) Another application of the complex hierarchy that we'll discuss is sparse polynomial interpolation, which we propose to solve via super resolution.
Host: Carleton Coffrin