Complex Polynomial Optimization and its Application to Power Systems

Event Sponsor: 
Mathematics and Computing Science - LANS Seminar
Start Date: 
Nov 13 2015 - 1:30pm
Building 240/Room 1404-1405
Argonne National Laboratory
Cedric Josz
Speaker(s) Title: 
PhD Candidate, Paris VI University
Daniel Molzahn

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, signal processing, imaging science, automatic control, and quantum mechanics. Complex numbers are typically used to model oscillatory phenomena which are omnipresent in physical systems. Thanks to recent advances in algebraic geometry, finding a global solution breaks down to solving a sequence of complex semidefinite programming relaxations that grow tighter and tighter. Well present numerical results on problems with several thousand complex variables and show that exploiting the complex structure enhances tractability. The problems consist of computing optimal power flows in the European high-voltage AC transmission network.

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