Venue/Online meeting link: https://meet.google.com/pba-nswy-fsc
Ph D Seminar - II Title: Dynamical system approaches to solve time-varying convex optimization problems Date: 14.02.2022 Time: : 03:00 P.M Venue: Google Meet Link: https://meet.google.com/pba-nswy-fsc Speaker: Ms. Rejitha Raveendran (EE17D016) Guide: Dr. Arun D. Mahindrakar Abstract A time-varying (TV) optimization problem arises in many real-time applications, where either the objective function or the constraints change continuously with time. Consequently, the optimal points of the problem at each time instant form an optimizer trajectory and hence tracking the optimizer trajectory calls for the need to solve the TV optimization problem. The work focuses on a dynamical system approach to solve TV convex optimization problems by analyzing convergence of the trajectories of a dynamical system to the optimizer trajectory of the underlying optimization problem. Prediction-correction algorithms are the frequently used approaches to track the optimizer trajectories of an unconstrained and equality constrained TV convex optimization problem exponentially. In the first part of the work we modify the existing prediction-correction dynamical system to achieve the convergence within a predefined fixed-time from all initial conditions. Later we propose a prediction-correction based projected primal-dual dynamical system to track the optimizer trajectory of a TV inequality constrained convex optimization problem with strongly convex objective function. Finally, we consider the TV extended Fermat -Torricelli problem (eFTP) of minimizing the sum-of-squared distances to a finite number of nonempty, closed and convex TV sets to illustrate the applicability of the proposed projected dynamical system.