March 10, 2022  – The Mezić Group is pleased to host Eduardo Mojica-Nava from Universidad Nacional de Colombia, Bogotá, Colombia

A recording of the talk is on our Youtube channel.

Eduardo Mojica-Nava from Universidad Nacional de Colombia, Bogotá, Colombia will give a Zoom seminar on Thursday, March 10, 2022 at 9AM PST.

Title: Koopman-based Learning in Continuous-time Optimization

Abstract: The operator-theoretic framework has emerged as a successful tool for data-driven learning of nonlinear dynamical systems. Koopman operator theory has demonstrated a strong connection between algorithms and dynamical systems. In contrast to the traditional dynamics of states, the Koopman operator is a linear infinite-dimensional representation on the space of observables. This new approach has brought capabilities for data-driven detecting of essential elements in global geometric analysis such as stable/unstable manifolds and invariant sets by means of spectral properties. On the other hand, saddle-point dynamics have become an important strategy in the design of optimal feedback controllers. In this talk, the Koopman operator framework is used to obtain a data-driven continuous-time optimization algorithm for solving constrained optimization problems using its connection with dynamical systems for numerical algorithms. Stability and convergence results are demonstrated for three different optimization problem cases: strictly convex functions, quadratic objective function, and nonconvex function with multiple saddle-points. Several numerical examples are simulated for illustrating the proposed approach.

Short Bio: Eduardo Mojica-Nava received the B.S. degree in electronics engineering from the Universidad Industrial de Santander, Bucaramanga, Colombia, in 2002; the M.Sc. degree in electronics engineering from the Universidad de Los Andes, Bogotá, Colombia; and the Ph.D. degree in Automatique et Informatique Industrielle from the École des Mines de Nantes, Nantes, France in co-tutelle with UAndes in 2010. He is currently a full professor with the Department of Electrical and Electronics Engineering, Universidad Nacional de Colombia, Bogotá, Colombia. He has been visiting professor at the University of Mons, Belgium in 2017 and Politecnico de Milano, Italy, in 2021. His current research interests include optimization and control of complex networked systems, operator theory method, switched and hybrid systems, and control in smart grids applications.