Accelerated Methods for Distributed Optimization Problems using Fixed-time Stability of Continuous-time Dynamical Systems

In this workshop paper, we present the recent developments on accelerated methods for solving constrained optimization problems using the notion of Fixed-time Stability (FxTS) utilizing the paradigm of continuous-time dynamical system. The notion of FxTS was first introduced in the field of control theory for studying fast convergence of trajectories of dynamical systems to their equilibrium point. We discuss how this concept can be used for optimization problems to solve them faster than the SOTA algorithms in distributed setting.