Session II.2 - Continuous Optimization
Poster
Hybrid methods for global optimization of large-scale polynomial problems
Gilles Bareilles
Czech Technical University, Czech Republic - This email address is being protected from spambots. You need JavaScript enabled to view it.
The Moment/SOS hierarchy provides a way to compute the global minimizers of polynomial problems, at the cost of solving a sequence of increasingly large semidefinite programs. We consider large-scale problems, for which interior point methods are no longer applicable to the SDPs.
We propose an algorithm that combines a first-order method on the SDP relaxation, and a second-order method on the polynomial problem. Interestingly, the switch between first and second-order method is based on a quantitative criterion, which ensures Newton's method converges quadratically from its first iteration. We apply this methodology to obtain global minimizers on optimal power flow problems of nation-wide scale.
Joint work with Johannes Aspman (Czech Technical University), Vyacheslav Kungurtsev (Czech Technical University), Jakub Marecek (Czech Technical University) and Martin Takac (Lehigh University, MBZUAI).