On the global minima of polynomial dynamical system identification problems

Solving nonlinear optmization problems is an important step in data driven system identification and machine learning. However, iterative methods do not guarantee to find the global optimum of these problems. The goal of this research is to acquire more insight in the optmization problems arising from system identification. To achieve this goal, a method is devised to find the global least-squares optima of identification problems for polynomial dynamical models. New mathematical structures are developed to represent the data. A ‘misfit-latency’ framework is also conceived to optimally map real, inexact data to these structures. This can be done using a multiparameter eigenvalue problem. Finally an algorithm is developed to solve these eigenvalue problems using methods from linear algebra, keeping in mind the challenges associated with large-scale problems. To reach these objectives, notions from Algebraic Geometry, Operator Theory, Sytems Theory and Numerical Linear Algebra will be used. For more information, see the attached research proposal.